HunnyPots - Has your daughter been tested for food allergies? Could she be allergic, not just intolerant? Either way, if you plan ahead where you want to dine call any of the WDW phone numbers and ask for the direct phone number to each restaurant you want to eat at. They will be more than happy to give you this information, especially if you explain your situation.
I have a few severe food allergies and must be VERY careful. When I am planning a trip to WDW I check out menus for all of the restaurants I am interested in. Since I am a pretty picky eater anyway I am usually able to go ahead and decide what I will be eating when visiting each restaurant. Then I schedule all of my meals, making PS where available. When I make my PS I inform them of my allergies. They always give me the direct phone number and ask me to call 3 days before my PS date to speak directly with the chef. Then, I call and talk with the chef or whoever is responsible for food allergy matters 3 days before my visit to that restaurant. Also, when I check in for my PS I mention my allergies (usually they beat me to it). Shortly after we are seated the chef comes out to talk with me and offer his/her ideas. The first time it was rather embarrassing because I felt like everyone was looking at my trying to figure out why I was so special to have the chef visit me. Then I thought about the consequences and decided that it was worth it. And we are all special anyway!
All of the chefs I have dealt with have been WONDERFUL. They have never acted like it was too much work for them or that I was causing them any problems. Sorry for the long post, but I thought I would give you all the information I could.
But to answer you question, with a little planning you should not have any problems!