Perfectly reasonable to think of NZ and Aus together! We share supermarket chains, banks, and hardware chains among many many other things 
But our mobile spectrum and networks are pretty separate, afaik.
I have a close friend happily using a FP5 in NZ with no issues.
Two of their networks Spark and 2Degrees are running their 3G networks until late 2025 so no VoLTE compatibility issues will be relevant for them until then. My friend is with 2Degrees.
Their third network One NZ seems to have shut down their 3G recently. I have no idea if FP5 works with them.
There’s definitely not been any panic about emergency calling over there yet, but it’s not really a concern until the last 3G network closes, so it could happen yet.