Once the cat leaves NZ it will have to go through the bio-security
import process unless the only other places you visit are
Australia and/or Norfolk Island. Otherwise the same importation rules apply. Most of the Pacific Islands are MPI Category 2, which can mean a quarantine of only 10 days, but worth speaking with them directly, especially if the countries you visit are on the "Pacific Islands" Category 2 list rather than the "Rabies-free" Category 2 list. I would recommend avoiding the Category 3 countries (I think only the Mariana's qualify in the Pacific region).
If you want to go down this road, then the absolutely best preparation you can do before leaving is to make sure the cat is microchipped, the chip is registered to you in NZ, and your vet has attached the chip number to all records. If that cat isn't chipped and you get one, try to get your vet to write a letter attesting that any records prior to the chipping apply to the animal in question. Make sure you understand where you can get a rabies vaccination during your travels so that you can have one within the required timeframe preceding your return.
https://www.mpi.govt.nz/dmsdocument/...dance-Document