Well at that time....is was a Naval War. The Imperial Japanese Navy was huge.
It seems that the "Naval Battle of Coral Sea" was the decisive battle.....as far as Japan encroaching upon Australia. Both the US and Australia took part in that battle.
Coral Sea battle took place in 1942....so pretty early in the War.
http://www.coconuttimes.com/articles/Remembering-WWII/The-Battle-of-Coral-Sea-
It was the first Navy battle between aircraft carriers...?
Any attack upon Australia.....by Japan, would have started with Aircraft Carriers....
Japan pulled a similar thing on the US...in Hawaii...and Pearl Harbor.
But that is an entirely different thing from an actual invasion...with troops.
I don't think Japan ever got close to New Zealand?