Hi A.,
Before you see the allergist, I suggest you try an elimination diet. The allergist will likely ask you to do this, anyway. First, unless your daughter has definitely shown a severe reaction to either wheat or dairy, I would add those foods back into her diet one at a time, and see if the symptoms stay the same or get worse. If they stay the same there's a good chance that you daughter is NOT allergic or sensitive to these foods (if she's truly gluten free, I think you can safely rule out Celiac disease). If the symptoms get worse when you add back a food, remove the food again. Once you've established whether or not these foods really are contributing to her problems, start eliminating other foods one at a time for several days. If the symptoms clear up, add the food back into the diet. If the symptoms return, you've found your most likely culprit. The most common food allergies in children are eggs (whites), soy, fish, tree nuts, peanuts, corn, wheat, and milk (usually cow's milk, but some milk-allergic people are also allergic to goat and/or sheep's milk), so I would start with those. Fruits high in salicylates also tend to exacerbate allergic reactions (if that is what this is), so you might want to include berries at some point in your elimination experiment. Other foods that tend to be allergenic include apples, peach, plum, cherries, kiwis, and avocado. Some people who are allergic to these and other fruits/veges can eat them safely when cooked, but not raw.
The tricky part of this process is that your daughter may be sensitized to multiple allergens, but not enough for each allergen to cause a reaction on its own. If this is the case, then she may need to be exposed to two or more items before an allergic response is seen. If this ends up being the case, it will be very difficult to figure out what (if anything) she is allergic to using an elimination diet alone.
You do not need to see an allergist right away for testing. Ask your daughter's pediatrician to order blood tests for specific IgE. Through discussion with you, the doctor can order the tests for the most likely allergens -- not just for the ones I've listed above, but also for allergens common to your daughter's diet and to your environment. Any positive result for a food allergen should be confirmed using an oral challenge, as sometimes IgE tests can be positive in the absence of a true allergic response.