If you also have a passport from another country you should always useyour Australian passport when leaving and entering Australia.
Australian citizens have right of entry to Australia and anAustralian passport is the preferred and most conclusive proof of thatright. Dual nationalsshould use an Australian passport to enter anddepart Australia. Other current passports can be used for travel whenoutside Australia if desired.
Permanent residents (migrants) cannot travel on their migrant visas once they have been granted Australian citizenship. This is because the migrant visa ceases to be in effect when Australian citizenship is acquired, even though it may not yet have reached its expiry date or been physically cancelled.
Australian citizens who hold dual or multiple nationalities must hold an Australian passport and use it to enter or leave Australia, even if they use a foreign passport overseas. The only exception is where they have been issued an Australian Declaratory Visa.