Any of BMus, DMus, TMus, LMus, MMus, or DipMus can get you on your way to a teaching career, when combined with at least a DipEd. You would, however, be best advised to go for the Con and snag yourself a BMus.
Oh, just so you know, the order is A, L, T, B, M, D (Dip doesn't really belong anywhere in there because it's not a "degree"). Associate, Licensiate, Teacher, Bachelor, Master, Doctor. Anything after BMus requires actual university study, though A, L and T can be done directly through the AMEB.
Dingo, who is that in your avatar? Your little sister? (seriously)