To be honest, I feel like the lack of identity of the invaders in Tomorrow, When The War Began probably improves the story. It's not a Tom Clancyesque war-porn thriller, and it's not really about "what if this particular country invaded Australia?". It's about war, and adolescence, and lost innocence. It always frustrates me to see people trying to criticize the books on the basis of a lack of realism.
As such, I think you really need to consider what you are trying to say. It's perfectly reasonable to make it "generic invaders" if that suits the story. The risk of going with a fascist Australian invasion is that the tale may slide into the humorous side of the Australia-New Zealand rivalry. Mind you... I'd still read it.