I'm strictly gluten free, and also need to avoid dairy, spinach, alcohol, and coffee. I've been able to eat almost anywhere we try at Disney. With only a dairy allergy, they should have no trouble accomodating you at either quick service or table service. Be prepared that you may only have two or three options for DS at some of the locations with smaller menus, but there will always be something. Many restaurants have allergy menus now that you can order directly from, and allergy orders should be identified differently with either a green colored tray and/or a wooden "allergy" pick in them, but it anything makes you feel uncomfortable you can always ask to speak to a chef or manager. Places without allergies menus (or if you have multiple allergies) will often bring you a chef either way. We like the allergy friendly chicken tenders and fries that are served at some of the quick service places at the parks. There are usually also healthier options like a chicken breast or fish, both for adults' and kids' meals. In terms of table service, we've always had good luck at most places. The only time I had bad allergy experiences at table service were at Wolgang Puck's in DS and Ohana (where the chef brought me a free creme brulee because it was gluten free but he forgot about the dairy. The he felt bad a replaced it with fruit and chocolate fondue...the chocolate also had dairy in it. Very nice of him, but not safe for me to eat.) For snacks, I highly recommend dole whip and popcorn from the carts which are both dairy free as of my last visit. There are lots of Popsicles and things too. All the Disney-owned snack carts should also have an allergy binder that you can ask to view which lists all the ingredients in a snack. I use this a lot just to make sure ingredients haven't changed from one visit to the next!
