DD is severely lactose-intolerant and can not even have butter or modified milk ingredients, etc. and all dairy has to be avoided for us. The non chocolate-dipped crispie treats were dairy-free when we were there in June... also popcorn from the vendors is dairy-free as are the adult hot dogs (and they are supposed to charge you for a kid hot dog since it is a dietary issue). Each food service local (minus the street vendor) has a list of foods with their ingredients. You should also compete the food allergy sheet before you go so the restaurants know you are coming and will have the chef come talk with you.
You can also e-mail the Disney Dietary folks any questions about specific foods before hand.
As the OP mentioned, Babycakes is dairy-free and the allears.net vegetarian list is good too.
Some TS restaurants are better about getting foods that are dairy-free AND the kids want to eat than others. One night all DD (not even 3 at the time) wanted for dinner was a hot dog and we were at Tony's. We said not to worry, pasta with Olive oil was OK and next thing we know she has a hot dog and they are not even on the menu!
Oh, and the gluten-free pizza is also soy cheese and pretty tasty!