Upvote:4
Yes, while you are in another country, i.e. not Australia or New Zealand, you are free to choose the passport you want to present.
Upvote:8
Yes. Both Australia and New Zealand recognise dual citizenship. Your New Zealand citizenship does not end simply because you have acquired Australian citizenship.
Your New Zealand passport remains valid until its expiry date, on which you can still renew your New Zealand passport. However, as an Australian citizen, you must now enter Australia using an Australian passport.