Non-dairy milk is pretty much non-existent at DLR, and they places that do have it (for coffee) have soy milk. So I'd bring your own shelf stable non-dairy milk of choice if your child drinks "milk." As far as table service, just note on your reservations the allergies and you'll be accommodated. For counter service there are no longer allergy lists at guests services, they suggest you go to each location and ask for their allergy binder. I'd recommend reviewing menus on Disney's site and allears (sorry, but the ones on this site don't get updated often) and seeing what might work and then ask at those locations what they can do. Most places that serve burgers and hot dogs will have a gluten free bun, so that will be a starting place for wheat. For dairy and eggs, I'd look at vegan recommendations. If something says it's vegan if you omit meat and cheese, you know you can probably just omit cheese. Just keep in mind that ordering allergy safe food will often take longer, so I would try sending a parent ahead to order when possible and bring your own safe snacks to avoid a situation where someone is starving and an order will take extra time.