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, other medical issues, 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.
Another great resource for you is a book called PassPorter's Open Mouse for
WaltDisney 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, including food issues.
You can also read Moms Panel advice on the related topic of food allergies
HERE,
HERE, and
HERE. I know that this is not exactly your question, but it may give you some additional ideas about how Disney might accommodate your daughter.
Good luck with your planning!