I brought my two small dogs over with me and they have settled in well. Just could not bear leaving them behind.
The good news is that the quarantine period is now only 10 days in NZ, which does cut down the cost.
There are companies in SA that specialize in moving pets all over the world, so you can contact one of them, and they will give you all the details. They will tell you what you need to do, book their flights, organize their travelling crates, etc. You can find one on the web nearest to you. They do not have to go into kennels in SA until just before they leave, but there are a lot of tests that need to be done first, (for rabies etc) but your local vet can probably do most of them. They also have to be micro-chipped.
There is a lot of paper work but the pet moving company will advise you on that. A lot easier than trying to do it yourself.
There are only 3 quarantine kennels on the North Island, two in Auckland and one in Levin, so depending on where you are going you will need to book them in beforehand.
Check out the links that other members have given you, but it is like immigrating, lots to do but so worth it.
Good luck with it.
