I have converted a NZ ATPL to Australian ATPL under the provisions of the Trans Tasman Mutual Recognition Agreement (TTMRA).
It was a paperwork exercise the cost quite a bit of money and time. The list of people that can witness your written declarations is quite narrow and in my case, I basically had to visit the country to get a federal policemans signature. No flight tests or exams. Australian CASA also required me to apply for a security ID card (ASIC) in order to see if I was a fit and proper person to hold an aviation document. You decare criminal history etc.
Australia would recognise my NZ Class 1 medical until it expired, but I elected to do a full initial issue Australian Class 1 before I came over.
I dont know if CASA will recognise a NZ licence where that licence was issued on the basis of some other foreign licence. It might pay to call CASA and check before you go down that track.