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You will love NZ.  They are very celiac friendly.  Wonderful people,
beautiful country, terrific food and it's inexpensive!
Christchurch has a huge info center in the middle of the town square
where you can ask about gf foods.  All groceries carry rice and corn
crackers/cakes and other gf foods as a matter of course.  I never loked
for bread but the B&B's we stayed in made special gf bread for me.
Eating out is no problem since everyone understands coeliac (the
European spelling) and is most accommodating. Have a ball.  We were
there for 6 weeks in Jan and Feb this year and I would go again in a
minute.

I returned from NZ last March.  My general experience was that no matter
where I was, I could go into a restaurant and explain my situation and
the kitchen was able to come up with a delicious GF meal for me.  I did
have one "accident," which interestingly enough, was in Christchurch.
My experience of Christchurch was limited to some jewelry shopping, and
there were no health food stores where I was.  Generally, supermarkets
carry things like GF bread.  There was a heavenly place we went to in
Kaikoura called Muscle Brothers -- the most exquisite muscles and
Pavlova, both GF.  Queenstown was lovely, as well as Milford Sound and
Te Anau.  To tell you the truth, we generally stayed in places with a
kitchenette so we could prepare our own food, but hardly ever felt the
need.  People in general have a greater understanding of celiac in NZ
than they do in the states.  I would be more worried about bringing
enough GF snacks for the flight -- I flew Qantas, and although they
provided a GF meal, it wasn't great, and most of the other things they
brought around to people were not GF.  Decaf coffee is not easily
available, and when it is available it costs a little more.  Have a
wonderful time.  I absolutely fell in love with NZ and hope to return
someday soon.

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