My son has multiple allergies and Disney is the best we have ever experienced in terms of helping us. Over on the Disabilities board, they'll be able to give you the number of a specialist you can call.
We tend to do table service, it's just easier with a kid with as many allergies as my son has. When we book the ADR, we tell them we have a diner with food allergies. They then ask us what he's allergic too...when I hit the 6th or 7th thing, they just say "I'll note that he chef needs to talk to you".
When we arrive, we also restate that we have allergies. When they seat you, the chef will come over and talk to you in depth about what the allergies are, what your child likes to eat and will then offer suggestions or (at buffets) will walk the line and tell you what is safe and what isn't. I know a couple times at the buffets the chef wasn't comfortable and cooked my son a special meal in the back. They have always been lovely.
If you have a fairly "standard" allergy, the counter service places have an allergy book you can reference. A manager can help you and you can request that the food is cooked to order for safety.
Good luck! Disney makes things magical for every guest, even those with allergies.