I was thinking of a different Australia. I agree with the socialist east and libertarian west but with some more stuff. Maybe a authoritarian socialist government (not communism, as in it still has some forms of capitalism, think modern China) in the east based in Melbourne and a libertarian government in the west centered in Perth. This could arise from a civil war in the late 30s after a socialist party democratically takes control of the government and the west secedes.
Perhaps the war could be from 1938 to 1941. An aboriginal autonomous territory owned by the libertarian west could exist in northern South Australia / southern Northern Territory. Victoria, most of New South Wales and southern Queensland would be "East Australia" while Western Australia, South Australia, north and parts of west Queensland and parts of north-west NSW could be "The Libertarian Republic of Australia", known as Free Australia to non-socialist countries and West Australia to socialist countries.
Adelaide could be split into west and east, with each side being highly militarized. Central Queensland (a region of Australia known for being far-right, the American South of Australia) could be home to many failed rebellions and constant battling on the streets, leaving it as a special area directly controlled by the East Australian government and ruled with an iron fist.
Free/West Australia is a key ally of the USA, which it is mainly based on.
I will post a map of my idea soon.