Most special diets can be accommodated at Walt Disney World. There is
an entire department at Disney Dining dedicated to helping guests with
food allergies, food intolerances, and
religious-based food requirements. Just send an email describing
your situation (at least 14 days in advance of your trip) to
SpecialDiets@DisneyWorld.com.
A cast member will get back to you with the information you need to
make sure that you have a safe, and delicious, visit to WDW.
In particular, nut allergies are very common. You can read Moms Panel advice on this topic
HERE,
HERE, and
HERE.
Another great resource for you is a book called PassPorter's Open Mouse for
Walt Disney World and the Disney Cruise Line. This sells for
approximately $20 and is available through amazon.com and many larger
bookstores. Open Mouse gives incredibly detailed information for Disney
guests with any sort of challenge, from anxiety to allergies and
everything in between.
Good luck and have a great trip!