Os países geralmente preferem que você deixe o mesmo passaporte em que entrou no país. É claro que isso nem sempre é possível (mudança de cidadania, por exemplo).
O Assuntos Internos notas do site para cidadãos duplos:
A dual citizen is a person who is a citizen of 2 or more countries.
You become a dual citizen if you:
are an Australian citizen, are granted citizenship of another country and don't lose your Australia citizenship, or
remain a citizen of another country and become an Australian citizen
Australia allows a person to have dual citizenship.
Claro, agora você sabe que eles o reconhecem.
E assim eles observam, independentemente, se você tem uma cidadania australiana:
Australian citizens entering and leaving Australia
Australian citizens should use their Australian passport to enter and
leave Australia.
The Australian Border Force has more information on crossing the
border.
If you have a passport from another country, you can use that after
you leave Australia.
A passport is the best way to show that you are an Australian citizen.
You might still be able to enter Australia if you are an Australian
citizen without an Australian passport, but it will be more difficult.
The airline might also stop you from boarding a plane to Australia.
Smart Traveller has more information about travelling as a dual
citizen.