Gidday
I live in Dunedin on the east coast of the South Island in NZ, and have some experience travelling around the bottom half of the country.
The South Island of NZ can be travelled quite comfortably in a sedan and give you access to many fnatastic photo opportunities. Many of the gravel roads can be comfortably covered in a sedan if driven sensibly.
If you intend to get off the sealed and major gravel roads then you may need to consider an AWD. Something like a Subaru Outback wagon should suffice. I tend to take an AWD when I get off the beaten track more for peace of mind, otherwise the sedan does fine. If hiring an AWD wagon is a comparable price, then I personally would take this option.
Just remember that NZ has a very variable climate. You will likely experience sun, rain, hail and possibly snow depending on where you are. We have had a lot of rain in the past month, so the ground is very wet in most places with plenty of mud.
If you have any more questions or want some info, let me know.
Cheers
Glenn