On the Aus licence you won't need time on type. The class rating system applies.
Lilflyboy is correct about IR being an added bonus for immigration purposes.
Make sure you do a BFR and medical just before you come over. Flying home to renew these is a very expensive process.
Do you know if you have to fly an NZ registered aircraft to get the type rating on your NZ licence? Or can an NZ instructor do the rating on a foreign reg aircraft (assuming they have a right to be PiC in that country)? There is a couple of kiwi instructors here (B-Cat and D-Cat) so that could be an option if required... Might be worth looking into