yeah i don't really think Japan could have invaded the whole continent...but hey...maybe through attacking key cities they could have forced the government to the table? Since a lot of the center of Australia is outback anyway.
You think?
That would be the only way i can see for Japan to defeat Australia.

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Never, never, never believe any war will be smooth and easy, or that anyone who embarks on the strange voyage can measure the tides and hurricanes he will encounter. The statesman who yields to war fever must realize that once the signal is given, he is no longer the master of policy but the slave of unforeseeable and uncontrollable events. -- Sir Winston Churchill