Hi, Michelle!
Great question!
We've traveled with relatives with food allergies (both children, one of whom has a tree-nut allergy, and adults) to Walt Disney World several times, and I cannot compliment the Cast Members and Chefs enough on how they handle such things. You'll be in good hands, as long as you take the time to do a couple of things.
First, be sure that the allergy is noted on your Advanced Dining Reservation; if you're not sure, simply call Disney Dining at (407) WDW-DINE, and ask the CM assisting you to ensure that the allergy is noted on each reservation you've made. Upon check-in, you should see "allergy" stamped on your slip, which will also let you know that your server knows about the allergy as well. Typically, the Chef will come out and discuss with the Guest (and parent, in the case of minors) which items to avoid. If you are unsure at any time, simply ask your server to double-check about the item in question, and he or she will be very happy to do so.
For more information about
special dietary requests while dining throughout Walt Disney World, click on that link. Again, be sure to speak with a chef at every Table Service restaurant you visit; they are always so accommodating, and welcome the opportunity to help Guests enjoy the meals that they've prepared for them. It's not a bother...they enjoy helping!
Send more questions as you think of them, Michelle; we love to help!