Many places have several options for gluten-free diners. There are eggs, fruit, breakfast meats, etc. Also, if you note on your reservation that you have GF diners, a chef will come to your table and tell you what is safe for you to eat. Many chefs will also offer to supply you with GF waffles or pancakes.
You might want to talk to the folks at the Special Dietary Requests Team:
Special Dietary Requests | Walt Disney World Resort
They should be able to answer even more fully!
Eileen