congrats on your acceptance to massey! i've also been accepted, although i'm not sure i'll be attending. i DID however look up the requirements to get a pet into the country, and this is what i found:
this site seems to be pretty comprehensive and accurate. it's too late now to start the process to bring your pet with you for july, but you should be able to get them over by the end of the year. you'll need the pet chipped, and to have a rabies titer drawn and sent out. then there are some additional vaccinations, and once in the country the pet will have to stay in a quarantine facility for 30 days, and then undergo additional in home quarantine. i estimate that each cat will cost around $2k all included (airfare, quarantine, shots, etc), with the price of the dog increasing with the size of the dog.
one thing that was very important to know for me, as a married woman, is new zealand's policy on pregnancy and staying in the country with a student visa:
1. if you are pregnant upon entering the country, you have to leave to have your baby. no excuses, no exceptions.
2. if you become pregnant in new zealand, and if your partner isn't a native kiwi with whom you can prove you are in a long term, committed relationship, you have to leave the country to have your baby UNLESS you have health insurance that covers pregnancy. none of the approved health insurance policies offered by massey cover pregnancy, so you'll have to get a supplemental policy prior to starting. this was extremely poignant for me to learn, as i realized that if i hadn't heard about it ahead of time, i could be forced - in the case of an unplanned pregnancy - to chose between my husband's child and my dream of becoming a veterinarian. not cool.
this policy was instituted a few years back to prevent a "drain on new zealand's resources" as people were coming in from other countries
specifically to have their babies in NZ where the health care was good and free.