Just got back from a gluten free trip to Disney. I was diagnosed with Celiac 10 years ago and so far, Disney is the best place to be gluten free. I've been 5 or 6 times since I was diagnosed.
That said, there aren't many options, there used to be more. Basically, at quick service you have choice of a burger with or without cheese/bacon, chicken fingers with fries or broc and maybe some sort of salad. Some places offer pizza, that I am guessing is Udi's.
Few and far between, you can find things like ribs or chicken, a sandwich on an Udi''s bun or a baked potato with butter, sour cream and cheese. Some places have pasta or rice. But you are more likely to find pasta at a table service restaurant.
Cooke's of Dublin is a counter service at Disney Springs. It is connected to Raglan Road and does a wonderful job with gluten free. They offer most of their fried foods as gluten free. Just remember to look for the green specks in the batter. They put parsley flakes in the mix so you know your meal is gluten free. Their skinny fries are out of this world.
The gluten free bakery at Disney Springs is as others have said, also dairy free and vegan. The cupcakes and, in fact, all of the baked goods are very heavy with an aftertaste. It is because they use only coconut oil. You must keep their baked goods in the fridge, otherwise they will melt. I don't mind them, as long as I have something to drink. Otherwise the flavor never leaves.
You can stop by Terra Treats at Animal Kingdom for some gluten free snacks. They will have Udi's muffins, bagels and I think, cookies. They also have bagged rice chips. They do not have cupcakes or hummus. Both are on the menu. They also carry gluten free beer and cider. But I am sure you aren't interested in that for your little girl.
I keep up with 2 different blogs. One blogger lives in Orlando. One just moved from there to an area near
Disneyland. You can find those blogs
here and
here. The second link, Sara, is also dairy free.
It has been very safe for me to eat at Disney. I've only been hit once, and we knew it right away because the server, then the manager, came right out and told me, before I even had a reaction. There was a blip in their procedure, but they have fixed it.