In my experience, Disney is wonderful with food allergies. Here are my suggestions...
1) Contact Disney Special Diets at
wdw.special.diets@disney.com
and let them know about your specific needs. They will send you attachments with general information and a form to fill out when you make your reservations.
2) When you make your reservations, either online or on the phone, make sure you check (or mention) the food allergy and check which allergies you have.
3) Fill out the form with your dining plans and email it back to Special Diets. They will then contact all the locations where you will be dining.
4) When you check in at the restaurant, make sure the reservation notes your allergy.
5) Usually your server will send the chef out to speak to you about specifics. If not, request that the chef come talk with you.
I think you will find Disney is one of the easiest places to dine with allergies. I hope you have as good an experience as we did.