There is a real baby boom on at the moment, and I guess it must be getting really hard for people to find a midwife. Last year when I had my baby, I had trouble finding a midwife too. I remember phoning around trying to find one when I was about 6 weeks pregnant, which is so early, and many were already booked up with clients. It must be even harder to find a midwife now. I reckon you'd need to book one as soon as you do the test!
Plus a lot of people don't know where to find a midwife. Here is a link to the search result on the white pages. You can narrow it down to find a midwife in a town near you.
Find Midwife: http://yellow.co.nz/whitepages/search/new+zealand/midwife-1.html
Some midwives work independent. Some work as part of a hospital or clinic. Some will visit you at your home during your pregnancy, most you will have to go to their clinic rooms for your visits.
This is usually the same midwife that is with you during labour, unless her "backup" is called, or unless you are using a hospital midwife service or obstetrician. So it is important to find a midwife that you click with, and that you like.