Hmm. This has a small section on what ANZAC does: https://www.axisandallies.org/forums/topic/35286/warfare-principles-of-axis-allies-by-andrewaagamer?page=1
But yeah, ANZAC usually just defaults to being extra troops for the US or UK.
I guess the good thing is that Australia is very far from Japan, so if the IJN is busy fighting the US Navy (or beating up India), you might be able to independently contest the Dutch East Indies or your National Objective islands (particularly the Solomons). It’s all very situational though.
I guess my best advice would be: Follow what the US and UK do and coordinate accordingly. The turn order means that the either power can can-open for you if given the chance.