My sister was just diagnosed with celiac and had to have gluten-free meals. Make sure to have Disney note that you need gluten-free meals on your reservation. At the podium, we always were asked if we did indeed have an allergy/intolerance and we said yes and they put it right on the card put on the table for your server. We were given numbers for the chefs at all the restaurants we were eating at and were told to call 72 hours in advance. If they do not pick up, just leave a message. Most were very good at calling back! They will be able to explain what you can and cannot eat. They also will try to work with you in what you will want to eat and will prepare special food. My sister ate better than she has eaten in months.
At your meals, a chef will come to your table as well to talk to you about your options. At buffets, the chef took my sister and dad (who is going gluten-free with her) around and showed them what they could and could not eat. If they were not able to eat specific foods and wanted something else, they offered to make it. They had special desserts, macaroni and cheese, etc. Ohana was the best by far, with the chef Kim (very nice guy), giving them the most personalized attention of any restaurant. They were able to eat basically everything that the rest of the family could eat, but it had to be prepared separately, with some different ingredients. Everything was very tasty they said!
My sister did have a little trouble with the counter service meals, just because she didn't bother to contact the correct people ahead of time and was just winging it. I don't recommend this. She was able to get gluten-free food, such as burgers/hot dogs/pizza, but she would have had a bigger selection had she talked to someone. We visited a few days after our real trip (we have APs), for a quick day while we visited my aunt in Florida, and ate at the Liberty Inn in Epcot, which my sister found to be the best counter service place for gluten free food. She spoke to a cast member there, who told her that she could get a list of all gluten free foods in each park if she needed it, and he gave her who to contact, which I don't specifically have... but I hear Brenda (whose e-mail is up there) should definitely be contacted.
Good luck and have a great trip!