Australia is geographically isolated, yes, but it's also in a very different sort of position compared to the US and UK.
The UK is an island nation off of a pretty wealthy continent and is in the middle of the trade routes between much of Europe and the Americas. It's a country quite literally in the middle of things.
Likewise, the US had easy access to European markets and was/is in between Europe and Asia, which comes with its own advantages.
Australia, meanwhile, is very very very very very far from its main markets in Europe and North America. Australia also just started off later demographically.
Here's an idea: nerf the British Empire elsewhere. Have the Dutch retain the Cape Colony after the Napoleonic war and have the Americans grab Upper Canada from the British (let's say the Treaty of Paris in 1783 settles the US border at the Nippising Line, meaning loyalists have to go elsewhere instead of Upper Canada). All those immigrants who wanted to stay in the empire but go someplace else end up in Australia.
Also, have Britain grab more territory in the area. Have Cook take New Caledonia on his expedition and the UK settle some loyalists there. Apply this same logic to Vanuatu, Fiji, Samoa, the Solomons, etc. Settle places, have the populations blow up, etc. Later on, when Australia is federated, all these places come together with the country (and of course, New Zealand is part of the confederation). Papua territory will probably be important as well. Maybe grabbing and colonizing the Kerguelen islands too.
When Britain and the Dutch are deciding how to divvy up southeast asia in the 1820s, have Britain get Sumatra and the Dutch keep Malacca (the inverse of OTL). The British main city in Sumatra was on the west coast, and I could see a Cape-Kerguelen Islands-Perth-Sumatra shipping route working well. Later on, Sumatra and Singapore are handed off to Britain.
Australia + Sumatra + Singapore + Kerguelens + New Zealand + Papua + Solomons + Samoa + Fiji + more settlers = Greater Australia.