. Once you have your new Australian passport the worlds your oyster. Me I put my passport in a safe little box along with my UK passport.
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This means that a person can hold nationality and the passport of both countries. As you can see for yourself an Australian ETA for British passport holders is easy to obtain. To get started visit this page.
If you have a passport from another country for example.
This means that a person can hold nationality and the passport of both countries. BUT when you left Australia you would need to leave on your UK passport - or else you would be subject to the laws regarding overstay fines deportation possible blacklisting. I too have dual British and Australian citizenship and two passports - Id take the advice given here and get yours renewed in person. If you give up Australian citizenship while overseas you might need a Resident return visa to re-enter Australia.