IMO, there's no better place to vacation and EAT if you or your child or someone traveling with you has a food allergy. My son is severely allergic to peanuts and I was very nervous.... But I was completely blown away by how seriously Disney restaurants took the situation. Every meal we had, the chef came out to speak with us...at the buffets, the chef walked me through the buffet personally and showed me what my son could and couldn't eat (And at Animal Kingdom, the chef even brought out a ton of peanut free goodies for him to have throughout the day)
I even received an unsolicited phone call from the food supervisors at the Spirit of Aloha dinner show shortly before our vacation just checking with me on the details of my son's allergy.
The servers are actually not supposed to even start taking your orders if you have a food allergy at your table until you speak w/the chef... (at least that's what we were told by several servers in various parks)
IF you are making dining ressies, ask that the food allergy be added to your reservation... and just mention it again when you arrive to be safe. As the previous poster mentioned, when you make ressies, they can and SHOULD give you the #s to reach the restaurants directly so you can speak with them ahead of time.
Yet another reason Disney ROCKS!