Disney is absolutely incredible working with dietary restrictions. In fact, I've never had anywhere pay such close attention to guests' needs.. As a former vegan, I had no difficulty avoiding animal products in any way, shape, or form while at WDW. However, it does take a bit of work beforehand. When I made all of our dining reservations, I made sure to have a notation included listing my restrictions, which included all dairy products like your daughter. Within a week of the trip, I called to double check that the reservations still included the notes and then reminded the cast members (who often double checked with me first) when we first arrived at the restaurants. Oftentimes, the chef actually came out and introduced him/herself to talk further with me. I felt pretty special!
At counter-service restaurants, this was a bit trickier because the menu was more set. If I had any question about the ingredients in the food, they could provide me with an ingredient list of every item.
To request the slipper dessert, I'd first contact SpecialDiets@DisneyWorld.com or call 407-824-5967. I"m also including a link to information on
Special Dietary Restrictions for Disney guests. I'm not certain about Beaches & Cream (sorry), but if you contact the above email/phone number, they can confirm the availability of alternative for your daughter..