The Air New Zealand pet policy is as follows:
Pets are not accepted in the aircraft cabin.
Air New Zealand allows domestic pets – cats, dogs, and small caged birds to travel as checked in baggage on all domestic services.
Any other type of domestic pet or livestock, or unaccompanied pet, may be transported as cargo.
Due to space limitations on Air New Zealand Link services (flight numbers in the 5000 and 8000 series), only one cage per customer will be accepted for travel as checked baggage. If you have more than one cage, then your pet must be pre-booked and travel as cargo.
Taking a pet to a foreign country involves preparation and planning far in advance of your departure date. Requirements for pet travel to a foreign country are set by the destination country. If you are you traveling to another country and bringing along your pet you’ll need to meet the animal health requirements of the country you are visiting.
More information on the Air New Zealand pet policy