There are a few Dames ( Dame Sylvia and Dame Susan to name a couple) about but I don't think they do pilots medicals.
You need either an AMA or a DME. A DME can do the examination but needs to refer your results to an AMA who then assess you as being fit. The AMA can do both roles.
Have a look here
CAA medical directory - New Zealand or here for overseas Doctors,
Directory of Overseas Medical Examiners you might find one near you.
Bill Daniels and Anton Wiles at Remuera Doctors do a good job.
Oh and don't forget the $300 donation to the CAA's christmas fund. You won't get anywhere until you've paid that.