I'm originally from NZ but now live in Luxembourg, and I know we found the whole system extremely frustrating when DS1 was first diagnosed with dairy allergy.
How serious are your DD's allergies?
I would take a very detailed list with you of every reaction she has had (trigger, symptoms, how it was treated, how long it lasted etc).
I guess the main issues for me would be finding out how serious the allergies are (if you don't know already) ie by doing skin prick and/or blood tests (I think the blood tests give more info), and making sure you have the right treatment. Depending on how serious the allergy is, you may want to ask for an emergency medical kit - we were not given this in NZ but as soon as we moved to France (when DS1 was 18 months old) they gave us the equivalent of an epipen, plus steroids, antihistamine and ventolin inhaler to keep with us at all times. I don't know how difficult it is to get one in NZ - we didn't ask because we didn't know about them.
Another issue to discuss may be childcare if you are planning to use any in the near future - the precautions you need to take and whether the childcare setting should have medications available for your daughter.
I would also discuss diet and ask to see a dietician who will monitor your DD's food intake and make sure she isn't missing out on essential nutrients (and maybe suggest ways of replacing them). One idea for replacing calcium which they didn't mention in NZ but did in France was to give bottled mineral water with a high calcium content.
What kind of milk is she on at the moment? this is another thing to discuss with the doctor, as you may be able to get hypoallergenic formula (eg Pepti Junior, Nutramigen, Neocate, depending on severity). Though to be honest they weren't keen on paying for it in NZ and told us to use rice milk or soy milk (personally I would investigate both of these before you go, as rice milk has relatively high levels of arsenic and it is now advised that it not be the main drink for children under 5, and soy milk has some issues with phyto-oestrogens which mimic the effects of oestrogen - nothing seems to be proven exactly but in France the advice was to avoid it is a main drink for young children, especially boys).
sorry if this sounds a bit negative about NZ, though I imagine you are coming up against the funding issues already anyway - and I think you are from the UK (based on Living Overseas threads!) so it may be similar there too.