A further recommendation:
I do not know the specifics (my memory is fuzzy) but at a meeting at a North American consulate a few months back discussing passports and visas, it was noted that it is a lesser known Australian Immigration idiom that it is illegal to exit Australia, if holding dual nationalities such as yourself, on the non-Australian passport - you must exit Australia on your Australian passport.
It was noted that it is not known how often this law/rule/requirement is actually utilised/asserted but I thought the information might be handy.