Take it.
Doing both islands, you will find plenty of opportunities to fly, there are many places away from people, national parks etc.
This page will have all the info you need to check what the rules are, there are no licence requirements for hobbyists (as yet).
www.aviation.govt.nz
You'll find the Airshare map link in there for NFZs etc.
Not shown on that is a ban on drones in all DOC (Dept of Conservation) National Parks, which are extensive on the south island west coast, Fiordland NP etc.
A shame, but then plenty of people go to those regions to escape.
There are no drone signs at many popular places to reinforce this.
Probably some local councils through NZ may have bans on drones operating from land under their authority, local parks etc, worth checking if you want to avoid any council ranger problems . . . but if you fly early, no people etc, you'd probably be ok with quick flights in coastal parklands etc.
Enjoy your trip, it's a bit of a nice place