DD12 isn't vegan but she is gluten, milk and egg free (among other things). She is quite the carnivore so most times her meals are meat based.
Lots of places carry gluten free pastas. These places also typically have allergy safe sauces.
Feb 2009 we stayed at Pop and the chef a few times made me the most AMAZING gluten free stir fry. We were discussing my meal and he mentioned that he had gotten in a fabulous order of fresh vegetables including some snow peas, beautiful mushrooms, fresh ginger, baby corns and so much more for a vegan guest and that he'd gladly do something up for me with them as well (I'm limitted in my meat consumption because I can't have beef or pork though I can do all other meats). The meals where he made that were probably the best meals I ate that whole trip and I think among my top meals of all of my WDW vacations.
Desserts and snacks were our biggest concern for DD12 since meals are pretty easy for a huge meat lover (slap a steak in front of her and she's happy). None of the packaged gluten free baked goods besides the Enjoy Life ones are vegan and EL is only found at very limitted places. Crystal Palace has a gluten free vegan brownie/chocolate cake and Chef Mickey has gluten free vegan cupcakes (vanilla and chocolate). At our resort, we had already spoken with a chef by phone ahead of time so there was a big batch of brownies ready for us when we arrived (we always eat at least 1 meal per day in our resort's food court). They also made an AMAZING gluten free, yeast free, vegan pizza that my kids loved (again, they did this based on my having spoken with a chef ahead of time so they were already prepared and only had to be cooked when we'd order). Itzkadoozie popsicles at all of the carts all over WDW are gluten free and vegan as is the popcorn. Sunshine Seasons should be able to do up a nice noodle vegetable tofu meal to order as well (they probably have a variety of options but you'll want to check with Special Diets about it).
We find that CS at our resort is so much easier than at parks with multiple restrictions. Sunshine Season at Epcot is likely the best exception though we still have yet to try it (I plan to during our upcoming trip). TS locations should be able to accomodate you much easier as well. If you can, try to get an ADR at 'Ohana as chef TJ's reputation for vegan as well as allergy friendly meals is legendary.
Make sure to contact Special Diets. Ask to have a chef from your resort call to speak to you if you plan to dine there much.