Hi Catherine!
Speaking from experience, one of the best things about Walt Disney World vacations is not worrying about where to eat! All of the restaurants there are extremely accommodating for those with special dietary needs. It really does take the worry out of dining!
While you really can't go wrong with any of the dining offerings for the Candlelight Processional Dining Package restaurants, Les Chefs de France and Le Cellier are my favorites. Via Napoli is a close third.
When you make your reservation, you'll want to make a note of the gluten-free dietary needs. A follow-up email to the
Special Diets group (Special.Diets@DisneyWorld.com) is also a good idea.
For more info on dining gluten free, a great resource is orlandoglutenfree.com.
Hope this helps! Have a great time and enjoy the show!