White Australia ended partly
out of necessity: you want to do ambitious post-war development, you need free workers to build the things. You
could have a POD where immigration restrictions are relaxed but at a minimum, with the migrant workers being third-class non-citizens and mistreated like in OTL Dubai. The further into the present that gets, the worse Australia will look.
Alternatively, Australia was still administering the Territory of Papua and New Guinea at the time - if they have to bring in foreign workers, Australia decides to use the 'natives' it already has and encourages/pressgangs them into coming over. In OTL Australia gradually gave more control to Guinea after the war; here, they need the cheap labour so they drag it out and they drag it out and they'll do it
soon and eventually they don't make an excuse. When the Guineas go to the UN, TTL's Australia tells the UN to back off.
And then you've got a white-majority developed nation that owns a non-white developing nation in the late 20th century, on top of the status of the aboriginals (their lot won't improve in a state that runs off indentured servants). Australia's not going to be a popular state but as long as the Cold War's going on, Canberra doesn't need to care too much because the US and UK will always have to back it!