Considering Australia feeds 80 million people and New Zealand maybe about 20, Australasia has plenty enough food to feed a population which would constitute a major world power. It is easy to forget that Australia is, you know, bloody enormous and that even a relatively arid place such as Australia is the size of the continental United States. It is going to have in absolute terms a lot of production. NZ for its part is certainly much smaller, but only a fool would levy a criticism of aridity towards those islands, which really are only small in relative terms.
The only big reason the population of Australasia is as small as it is is due to the lateness of its colonisation and the need to compete with the Americas, much closer and well known, for its immigrants. People simply did not migrate to the other part of a world without a huge incentive. In the first 60 years of settlement Australia reached a mere 350 000 people. Why? Well why on earth would people go so far when the far more developed Americas are right across the Atlantic? The one thing which did bring people here was the enormous Gold Rushes, which tripled the population in a decade, but even these can only go for so long. Australasia simply was not a particularly viable place for population growth until relatively recently (the 1860's) if we are comparing it to the New World.
Furthermore, Australia and to a lesser extent New Zealand are significant powers. The South Pacific is entirely our domain, no one bar the United States could contest that and nor will they. Australia in the South Pacific is a more power state than either the UK or France, despite these nations having significant interests there, and influences are vast albeit relatively sparse and watery portion of the globe. One might argue well that this is simply due to their being no one else about, and to an extent this is true, but such an argument would then bring into question whether the United States in the 19th century was the dominant force in the Americas, for instance.
There are certainly ways to create a much more powerful Australasia, but I think that you'll find they are somewhat limited without an early POD, depending I suppose on just how 'major' you're looking for in a global sense. The easiest IMO is an early gold rush. The Victorian Gold Rush was simply a matter of waiting until a few people ambled into Central Vic and finding the first of something like 12 million tonnes of gold sticking out of the ground and allowing the word to spread. IOTL. it took 16 years of permanent settlement in Port Phillip for this to occur. Melbourne was founded in 1835, the gold rush began in 1851. If, hypothetically, the 1803 settlement at Sorrento was moved to the Yarra in northern Port Phillip then it is quite possible that the gold rush could be moved forward decades. I suspect that a convict settlement might take longer to explore the interior than a predominantly freely settled colony, but lets say that by 1830 the Victorian Gold Rush has begun.
Historically in the first year of the Gold Rush the Australian population doubled. This however was in conjunction with the very slightly earlier Ophir Gold Rush in NSW. I personally don't see a way to speed up the necessary penetration of inland NSW even if the Blue Mountains are passed earlier (which in itself is very easy to do), as without the necessary infrastructure NSW is a much more challenging place than central Victoria in terms of people wandering about. As such Ophir I think should be let out of the ATL gold rush for now.
Nevertheless, over the course of the 1830's the population in Victoria is likely to go at similar pace as historically, and at some point the gold fields of NSW are likely to be reached if not from the east then the south. This somewhat slowed and early gold rush has some interesting consequences. The dominance of Melbourne* for instance will be even more total than OTL's 19th century. If Ophir and others are reached from the South (not a given mind you) then potentially a much more settled Murray-Darling region could occur. The other state's gold fields will be reached at much different paces. The butterflies are enormous, but essentially what the earlier gold rush will do is create a well developed Australia maybe 20-30 years sooner than OTL, with an urban and industrial as well as agricultural economy to attract settlers. Furthermore, as Australia's larger population will necessarily create larger natural growth for much longer then there's that too.
Where such a state could develop is of course a timeline sized piece of research, but here are some other ideas for how much larger the population could be and what this could mean -
1) An early development of the Oord River and perhaps parts of the Kimberly could produce a much larger population in the Top End. Technically very possible, though historically this region was neglected due to its climate. Still very doable though.
2) Somehow neuter aspects of the White Australia Policy(ies). This was essentially born of the gold fields, and a place like Australia is likely always have some racial immigration restrictions during the 19th century, but it is far from pre-ordained and attracting wealthy and skilled Asian immigrants could be a useful boon, though not a game changer.
3)Early settlement of the rest of WA. WA was not really settled until the 1890's with the gold rush there, but was in fact founded before Victoria. If somehow the gold of the interior was found earlier, and considering it took 60 years IOTL I do not see this as a real problem, then like Vic it could grow much faster and sooner.
4) Earlier discovery of the South Island Gold. My NZ history is rather lacking compared to Aus, but gold is the sort of thing that's always there until it's found and I don't see any real reason that it cannot be found sooner in South Island. This like elsewhere in the region could lead to a much earlier proper settlement of NZ, which in turn could lead to it actually being developed enough to attract more settlers and not being an overseas hinterland for Australia until the 1890's.
There are doubtless plenty more things which can be done to improve growth in the region, though probably not on the same scale as the above. What might this actually mean in a modern sense? It is very hard to say, as pushing the POD back to 1803 utterly changes the world. In isolation, though, and making the assumption that Australasia is allowed to develop in a manner not too dissimilar to OTL only earlier, then it is quite possible to see a combined population of about 60 million (say 45 Aus, 15 NZ) by the turn of the millennium, though this is being very optimistic. This is more than enough to be a major power on the level of a Western European country, though still pails in comparison to the (often latent) power of our Asian neighbours and of course the United States.
What this part of the world needs more than anything else in developing is simply the time to do it. While NZ currently struggles with growth due to it simply being too small and with a limited economy, Australia has been growing by 2-2.5 million people a decade since WW2. In the 50's this was a 20% rate of increase. Actually having said that I think we cracked 3 million in the 2000-2010 period. We are growing fast and faster, but we simply haven't been growing for long enough. Speed this up by some decades, giving more time before the demographic transition and more competitiveness in the great periods of migration, and our growth can be amped up a lot.
The only big reason the population of Australasia is as small as it is is due to the lateness of its colonisation and the need to compete with the Americas, much closer and well known, for its immigrants. People simply did not migrate to the other part of a world without a huge incentive. In the first 60 years of settlement Australia reached a mere 350 000 people. Why? Well why on earth would people go so far when the far more developed Americas are right across the Atlantic? The one thing which did bring people here was the enormous Gold Rushes, which tripled the population in a decade, but even these can only go for so long. Australasia simply was not a particularly viable place for population growth until relatively recently (the 1860's) if we are comparing it to the New World.
Furthermore, Australia and to a lesser extent New Zealand are significant powers. The South Pacific is entirely our domain, no one bar the United States could contest that and nor will they. Australia in the South Pacific is a more power state than either the UK or France, despite these nations having significant interests there, and influences are vast albeit relatively sparse and watery portion of the globe. One might argue well that this is simply due to their being no one else about, and to an extent this is true, but such an argument would then bring into question whether the United States in the 19th century was the dominant force in the Americas, for instance.
There are certainly ways to create a much more powerful Australasia, but I think that you'll find they are somewhat limited without an early POD, depending I suppose on just how 'major' you're looking for in a global sense. The easiest IMO is an early gold rush. The Victorian Gold Rush was simply a matter of waiting until a few people ambled into Central Vic and finding the first of something like 12 million tonnes of gold sticking out of the ground and allowing the word to spread. IOTL. it took 16 years of permanent settlement in Port Phillip for this to occur. Melbourne was founded in 1835, the gold rush began in 1851. If, hypothetically, the 1803 settlement at Sorrento was moved to the Yarra in northern Port Phillip then it is quite possible that the gold rush could be moved forward decades. I suspect that a convict settlement might take longer to explore the interior than a predominantly freely settled colony, but lets say that by 1830 the Victorian Gold Rush has begun.
Historically in the first year of the Gold Rush the Australian population doubled. This however was in conjunction with the very slightly earlier Ophir Gold Rush in NSW. I personally don't see a way to speed up the necessary penetration of inland NSW even if the Blue Mountains are passed earlier (which in itself is very easy to do), as without the necessary infrastructure NSW is a much more challenging place than central Victoria in terms of people wandering about. As such Ophir I think should be let out of the ATL gold rush for now.
Nevertheless, over the course of the 1830's the population in Victoria is likely to go at similar pace as historically, and at some point the gold fields of NSW are likely to be reached if not from the east then the south. This somewhat slowed and early gold rush has some interesting consequences. The dominance of Melbourne* for instance will be even more total than OTL's 19th century. If Ophir and others are reached from the South (not a given mind you) then potentially a much more settled Murray-Darling region could occur. The other state's gold fields will be reached at much different paces. The butterflies are enormous, but essentially what the earlier gold rush will do is create a well developed Australia maybe 20-30 years sooner than OTL, with an urban and industrial as well as agricultural economy to attract settlers. Furthermore, as Australia's larger population will necessarily create larger natural growth for much longer then there's that too.
Where such a state could develop is of course a timeline sized piece of research, but here are some other ideas for how much larger the population could be and what this could mean -
1) An early development of the Oord River and perhaps parts of the Kimberly could produce a much larger population in the Top End. Technically very possible, though historically this region was neglected due to its climate. Still very doable though.
2) Somehow neuter aspects of the White Australia Policy(ies). This was essentially born of the gold fields, and a place like Australia is likely always have some racial immigration restrictions during the 19th century, but it is far from pre-ordained and attracting wealthy and skilled Asian immigrants could be a useful boon, though not a game changer.
3)Early settlement of the rest of WA. WA was not really settled until the 1890's with the gold rush there, but was in fact founded before Victoria. If somehow the gold of the interior was found earlier, and considering it took 60 years IOTL I do not see this as a real problem, then like Vic it could grow much faster and sooner.
4) Earlier discovery of the South Island Gold. My NZ history is rather lacking compared to Aus, but gold is the sort of thing that's always there until it's found and I don't see any real reason that it cannot be found sooner in South Island. This like elsewhere in the region could lead to a much earlier proper settlement of NZ, which in turn could lead to it actually being developed enough to attract more settlers and not being an overseas hinterland for Australia until the 1890's.
There are doubtless plenty more things which can be done to improve growth in the region, though probably not on the same scale as the above. What might this actually mean in a modern sense? It is very hard to say, as pushing the POD back to 1803 utterly changes the world. In isolation, though, and making the assumption that Australasia is allowed to develop in a manner not too dissimilar to OTL only earlier, then it is quite possible to see a combined population of about 60 million (say 45 Aus, 15 NZ) by the turn of the millennium, though this is being very optimistic. This is more than enough to be a major power on the level of a Western European country, though still pails in comparison to the (often latent) power of our Asian neighbours and of course the United States.
What this part of the world needs more than anything else in developing is simply the time to do it. While NZ currently struggles with growth due to it simply being too small and with a limited economy, Australia has been growing by 2-2.5 million people a decade since WW2. In the 50's this was a 20% rate of increase. Actually having said that I think we cracked 3 million in the 2000-2010 period. We are growing fast and faster, but we simply haven't been growing for long enough. Speed this up by some decades, giving more time before the demographic transition and more competitiveness in the great periods of migration, and our growth can be amped up a lot.