Hi Shannon,
Disney does a wonderful job accommodating guests who have dietary needs. They are so accommodating that my shellfish allergic daughter can eat at a traditional clam bake and be totally fine.
The
Hoop-Dee-Doo Musical Revue is such a fun show. It has a set menu of fried chicken, ribs, salad, baked beans, cornbread and strawberry shortcake. However, the Trails End Restaurant is right next door so I do not see why they would not be able to create something for your child.
I would call Disney Dining at 407-WDW-DINE and ask that question. This way you can figure out if the options available would be something your child would like to enjoy.
Remember to note the gluten allergy on all of your dining reservations so you can have your child's meals taken care of at each restaurant.
Wishing you a magical vacation!
Beth