Australia today could support 60+ million people without any changes to its agriculture; watering them is relatively easy compared to the water needed for that same agriculture/industry. It could be achieved without any particularly expensive infrastructural changes such as water tanks/people living in the North/North-East. The specific number that would have been possible between 1900-1965 is debatable, but it's reasonably likely that a population of at least 20 million or more would have been possible from the turn of the century onwards. Getting those people is the trick.
One way would be to simply increase immigration from Europe, in particular British immigration which was acceptable to Australia at the time. Even better would be to somehow make North America unattractive to this immigration, perhaps a combination of stricter post-WW1 immigration restrictions in the US and Something Bad happening in the UK to encourage migration?
The other obvious but difficult method is to reduce prejudice against other Europeans or even Asians earlier. How this is done at this late date I don't know, at least done in time for a significant change for 1965, but reduced migration restrictions/prejudice on arrival would create a much larger pool of potential migrants. And once the population is there, greater power will follow. Like Japan, Australia has the advantage of being far from any rivals and its relative power would be magnified in the South Pacific. Even with 20 million people in say, 1940, Australia would probably have more capacity to influence all of south east Asia than any European country, at least on a material scale if not political.
might persuade them to throw in with the Central Powers. Which could end up with Dutch East Indies being mandated to Australia after WW1.
