Oz as a a Great Power
I don't think it is possible, but what would be possible would be to give Australia a much larger population and greater industrialization at the start of the 20th C.
If Cook, on either his First or Third voyages, had discovered Bass Strait (he was either side of it) and the first colony was established on the north coast of said Strait. Port Jackson was established in an attempt to replace the naval stores situation that the Empire had lost due to US independence. What Britain was looking for was a source of naval stores that was in their control, and available all year round, even if it took longer in transit.
Prior to the end of the Seven Years War much of Britain's naval stores come from North America, and much of the rest came from the Baltic. With the loss of NA's all year round ports, and the continuing possibility of interdiction of the Kattegat and Skagerakk Britain required another source.
Unfortunately, Port Jackson and the Sydney Basin are absolutely useless as sources of naval stores. However, what is now Gippsland in Victoria would have been a great source, it would have been between 3 and 8 weeks closer time wise, and just to top it off, about the time Blaxland, Wentworth, and Lawson were finding a land route out of the Sydney Basin (1812) they would probably have been finding gold in the central highlands of Victoria.
By the time news of this discovery got back to England the Napoleonic Wars were ending, England was in serious need of an injection of bullion into her vaults, and there were tens of thousands of veteran soldiers who had no other careers or training, and lots and lots of ships that were about to be laid up and sailors thrown ashore. Can we say gold rush, folks.
Additionally, the first few years after the end of the Napoleonic Wars saw a series of poor crop years with much hardship across all of Europe. This would have been another incentive for a population influx, especially if Britain was providing and subsidizing transport.
With a major population influx added to shipping construction along the coast of Bass Strait, and the availability of coal, iron, copper, tin, lead, etc within the area would have provided a strong basis for a rapid industrialization. When gold was discovered in 1949 in California much of the mining population and supplies would have come from Australia, as it would have been quicker and cheaper to bring them from there than the US east coast and Europe.