We went to Disney FL with my son who is 5 and has sensitivity to wheat and dairy. His is not life threatening. Disney was very accommodating, it is better to eat in the sit down resteraunts, but we did not do that, we were staying in a condo nearby, on a budget, and mostly ate there.
We did eat at the park several times though. They have an allergy hotline where you can call and tell them the allergies and they can tell you where to eat that is safe. At the burger place in tomorrowland, can't remember the name, you can ask for the manager and they had all sorts of accomodations. Great company.
Have fun.
Jen