This is what it says on the cake thread on the top of this page, but maybe ask in there.
"What if someone in my party has dietary restrictions?
In general, Disney will do its best to accommodate dietary restrictions like allergies, but it’s best to call to find out your options. Usually they will refer you to vegan bakery Erin McKenna’s Bakery(née Babycakes NYC) at Downtown Disney, which delivers two-layer 6-inch cakes (serves 8–10) to restaurants on Disney property for $52. The price of the cake is $59 if you pick it up at Erin McKenna's.
Call 407-938-9044 to order (Monday – Friday, 9am–5pm). Erin McKenna’s offers gluten-free, wheat-free, soy-free, casein-free, egg-free, vegan and kosher baked goods. Certain other Erin McKenna’s Bakery items—like mini cupcakes, cookies and doughnuts—can be found in the gift shops at the Beach Club and Kidani Village; at Jambo House’s quick-service spot, the Mara; in the food courts at Pop Century and Art of Animation; and at Animal Kingdom’s Gardens Kiosk, a food-allergy info booth near Flame Tree Barbecue and It’s Tough to Be a Bug."
I have ordered gluten free birthday cakes direct from Disney and had them delivered to the resort. I believe I picked the cake up in the food court. This is going back a few years, before Erin McKenna's was around.
It depends on which resort and what you are looking for. Many times they will refer you to Erin McKenna's which does not deliver to resorts. But I have in the past had luck with ordering a gluten free cake if it comes from the Contemporary Bakery. Not all bakeries are willing to make them, but it may depend on who you get when you call to order. They used the Namaste gluten free cake mix and the only options were vanilla or chocolate. Of course their bakery is NOT gluten free so keep that in mind if cross contamination is a high risk. Erin McKenna's on the other hand is a gluten free bakery.
Start with the cake hotline and see if you get anywhere.
Gluten free cupcakes seem to be available in most restaurants but you have to ask about them.
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