As far as AK goes I have a few suggestions..
Flame Tree BBQ has a really great fruit plate, btw. Obviously, the yogurt they serve is not vegan, but you can either ask them to hold the yogurt or maybe someone else in your party might enjoy it. It was a vanilla honey yogurt if I remember right and my son loved it. The fruit was very fresh and plentiful. Definitely something I enjoyed and would be great on a warm (hot) day.
I did try the veggie sub from Restaurantosaurus and thought it was quite good. The veggies were grilled and it was a nice change from a veggie burger. I will point out that there is cheese served on the sandwich, so your daughter might want to hold the cheese. The toppings bar is also good, it's nice to be able to add some fresh tomatoes or lettuce to the sandwich.
I will note that I am a ovo-lacto vegetarian, so I wasn't paying a lot of attention to buns served with the sandwiches and/or veggie burgers, but I do know you can request them at the time you place your order.
Sunshine Seasons is my favorite CS in Epcot. The tofu noodle bowl is probably something I could/would easily eat at least once a week forever.

Every time I try to branch out and try other veggie options I actually regret not ordering the noodle bowl.
There is a vegan/vegetarian thread here on this forum that might be helpful to read through. And plenty of nice people to help answer any questions you might have.