My DH is wheat intolerant, and a good friend of mine is a Coeliac. She gets quite a lot of wheat-free stuff on prescription, I don't know what the situation is in NZ for that?
DH and I lived in Sweden for quite a long time, where the availability of wheat-free products is also quite poor (although what you could get was generally of better quality than the stuff in the UK). This led us to have to improvise and we mostly cook everything from fresh now as then you know exactly what you're getting. Delia is of course a godsend for this, and it's fairly easy to adapt some recipes that call for flour or breadcrumbs, substituting with corn flour or rice. My other fave website was the Weightwatchers Recipe ones, as you can simply tick a box to search on wheat-free or gluten-free. But you need to be a WW member for this.
Eating out is a tricky one, but your local Coeliac Society should be able to help you out a lot.
Making wheat-free bread is a bit of a pain (mainly because it's hard to keep it moist enough to be palatable) but it can be done, although we just tend to substitute with other carbs like potatoes and rice.
If you're buying processed stuff, it's really a question of reading every label carefully. (At least you don't have to do it in Swedish without speaking the language!). As well as wheat flour, we avoid modified maize starch as it's often been modified with wheat (so they tell me in Sainsburys anyway), and MSG.
Hope things go okay, foul smelling poo is a symptom of Coeliacs but as you say, it's all pretty foul smelling! I guess to rule out the possibility of it being yeast rather than wheat, you could try your little girl on yeast-free bread (soda bread?).