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What would have happened is Westralia really had managed to ceed from Australia
In my opinion:
Westralia joins WW2 and fights alongside Australian and other commonwealth troops.
Westralia signs the Canberra pact with Australia and New Zealand
Maybe Westralia gets imvolved in Vietnam and Timor as Australia did IOTL alongside Australia
But could Westralia have bigger impacts on history? Could it lead to a breakup of the Australian Commonwealth into several smaller Dominions? And if so what effect would this have latter with a growing Indonesia (Wich may be able to expand more easily into Timor and maybe Papu New Guinea?)