I haven't been able to pin down about the dog license in a way that I can quote to you, but I suspect licenses are required in NZ. Most information seems to hark back to individual councils and bye laws so perhaps you'd need to know which area you intend heading for.
Meanwhile, whilst digging around, I found this
NZ doggy site which might possibly be of interest to some of you pooch owners. If you go to General Pet Travel at the top and click on the links underneath, it gives suggestions for dog-friendly hotels, motels, kennels and campsites.
Edited to add, you might find something useful in
The Dog Control Act 1996 .
Changes to the 1996 Dog Control Act .