NZ is great for touring around in a camper, there are freedom camps [free!!] DOC sites [cheap] POP sites [cheap] and main campsites [dear]. As been mentioned, plenty of people buy an estate car or MPV, throw a mattress in the back and do the tour on the cheap. Be aware that most DOC sites and Freedom Camps will fine anyone without a Self Contained certificate, got to say though, it wasn't very well policed.
Hiring campers is expensive, we were quoted by both Britz and Maui £25k for 6 months, however, we paid £9k renting from Advenurevans. BUT, don't rent from them, long story, but just don't.
We found the people very warm and friendly, the scenery is jaw dropping, the roads can be a bit challenging in some areas but that's part of the adventure.
Rankers.com and Campermate.com are brilliant apps for finding campsites, supermarkets, garages etc etc.
The only negative for you. Your daughter may not want to come back! The first words my daughter said to me when i met her at the airport following a holiday there was "I am going to live in NZ". And that is exactly what she is doing now and has applied for residency.
Good luck to your lass.