Nattylou has a great idea. Talking to a pet company will help alot.
I brought my cat's from NZ to Australia and it cost me $500 per cat to fly them through a pet travel agency. This was twice the amount of my flight so it's an expensive process. The reason i went through an agency instead of doing it by myself (i'm not sure which is cheaper) was
a) couldn't find enough general information
b) too many fiddly details to sort out & if you miss out one thing, or getting something wrong it can result in your pet on not being able to fly with you and having to start the costly process all over again.
It can be a long process and it would be made much easier if you got an agency to do it for you. Pet importation from NZ to Oz and back is fairly easy as both countries allow them to fly in and back freely without quarantine as long as they are looked over by a MAF vet before departure and on arrival, but i am not sure what requirements are of your pet. Most agencies will also supply you with a air carrier for your pet (they have to also be of a certain standard - meet height regulations etc) and they can also try and get your animal on the same flight as your self as long as you are flying into a major port (we flew from Hamilton airport, not a major airport therefore our animals were unable to accompany us and had to fly from Auckland). Also make sure you do checks with the airline you are flying with on their policy in regards to travelling pets, and ask what they keep the temperature in their holding area on the plane as some will treat them like baggage and will leave them in freezing cold temps - imagine what will happen if they are kept in those conditions on a 20 hour flight.... i have heard some gory stories which made me double check with my airline. I even reminded them when i boarded my plane and reminded the air hostesses on board. LOL