Disney is my favorite vacation place for a variety of reasons, but being able to easily eat dairy free is near the top of the list. There are so many options and it's so easy to find out what is available without dairy everywhere you go. The allergy menus at the quick service stations are very helpful. There is usually a cast member standing by with regular menus and allergy menus. Most restaurants have special allergy menus now even the buffets. The chefs are always available to speak with you personally and if it is a buffet to walk the buffet line with you to show you what to enjoy and what to avoid.
Mickey pretzels, regular popcorn from the popcorn carts (and I've been told the maple popcorn in Canada at Epcot), all the Dole Whip flavors (just make sure nothing is swirled with vanilla soft serve), the sugary almonds, LeFou's Brew, Kaki Gori, SORBET at L'ARTISAN De GLACE in the France Pavilion, a vegan cupcake at Sunshine Seasons that is filled with pineapple.... and several other snack options.
Congratulations on working through your recovery and being open about it. I don't know of a particular thing to do as far as celebrating while you are getting the snacks because it's such a personal victory. There is a Lost Princess cone that is a lemon flavored Dole Whip. It comes with an edible flower and represents Rapunzel. Since you are out there living your new dream, maybe that would be a good celebratory thing to try.
Best Wishes!