Julia, you need to start from the beginning with your father's birth certificate (if looking for Quayle ancestry), as this will give his parents' names and other information. If this was in NZ you can buy an uncertified photocopy for a cheaper price. Then get his parents' marriage certificate, now that you know their correct names, and from that you can buy your grandfather's birth certificate. When you get back to the earliest one who went to NZ you can find his passenger record from indexes and from knowing how long he had been in NZ from the certs. Death certs will also help, but it is one step at a time. If the earliest immigrant came from the IOM the address there is often given in his children's birth certs.
The same process applies if your father was the immigrant - starting with his birth cert.

If you have had 2 or 3 or more generations in NZ these indexes will help once you have got back a couple of generations:
www.bdmhistoricalrecords.dia.govt.nz/Home/
www.archway.archives.govt.nz/
freepages.genealogy.rootsweb.ancestry.com/~shipstonz/cemeteries.html
paperspast.natlib.govt.nz/cgi-bin/paperspast

- But don't jump ahead. Get all the information about one generation (including siblings where possible), before moving back to the previous generation, and obtaining all the birth/marriage/death certs you can find for them along the way.

We can help with IOM records once you have the name and rough age of the person who emigrated.
Let us know how you go.

Sue