Yes, I believe you can. There is an agreement between NZ and Australia, accepting each others education as equal. You will still need to get registered in Australia after receiving NZ registration, but it is just a formality and a cost.
You should, however, speed up you registration efforts for NZ, if you plan to do so. They are rather strict on career breakes and don't accept any break longer than 3 years. Good luck.
Cheers,
Fyzzio