Hi Kate,
google is your friend. If you put in "Physio, nz", the first hit is the NZ Physio Association, the second one the Physioboard.
You need to register with the NZ Physiotherapy Board. Go to "For Physiotherapists", then "Registration", then "Overseas Qualified Physiotherapists" and you will find all the information you need. It's not a long journey, it's pretty straight forwards.

Applying for Registration | Physiotherapy Board New Zealand

Good luck,
Fyzzio