To avoid any troubles on this trip, you should enter Japan using your Australian passport.
Now, regarding being a dual national is technically illegal, and your comment to the other post:
There was one news article that said that Japan had never actually enforced the dual citizenship rule and stripped a person of their Japanese citizenship but a lot of anecdotal comments in forums seem to suggest otherwise (making a person choose a citizenship on the spot at the airport or at embassies) which I found a bit worrying.
If you were born to Australian-Japanese parents (which I think you were), you must choose either nationality before reaching 22 (in "choose" I mean to report to the authorities, and in either case you must report to the authorities). Since Japan does not permit the dual nationality, if you choose Australian citizenship, or more correctly, if you don't renounce your Australian citizenship by reporting to the authorities, the Japanese government might treat you as having renounced Japanese nationality.
In that case it is possible that your Japanese passport gets deprived, because it implies you are having the Japanese passport illegally. (but don't get afraid; this is extremely rare.)
That being said, the law is pretty lax and exists just for the sake of bureaucracy. This year the head of the opposing party was found to have the dual nationality (i.e. she didn't report to the authorities which nationality to choose) but she didn't get arrested nor even fined. She eventually renounced her Chinese nationality, though. (And she keeps being a politician, even though Japan does not allow any foreign citizen to become a politician).
For more information, check out the following pages: