I think the only thing I've ever eaten at AK is a cookie (a really yummy one, but just a cookie) from one of their snack carts. I'm wondering if its worth it to leave and head elsewhere for lunch or just hold off and then hit downtown Disney.
Why hold off or go through the trouble of leaving in the middle of the day? Why not try Flame Tree BBQ? It's getting terrific reviews.
There is very little vegetarian friendly food at AK.
I actually think the vegetarian selection is pretty good at AK. You should do TS for your best options.
Pizzafari - cheese pizza
Rainforest Cafe - veggie burger, a number of salads, plant sandwich, passport to paradise pizza, hong kong stirfry without meat
Restaurantosauraus - veggie burger
Tusker House - a number of salads, preserves, tabbouleh, hummus, baba ghanoush, couscous, fruit, a whole vegetarian table, veggie sides
Yak and Yeti (TS) - salads, lo mein without meat, stir-fried beef and broccoli, veggie sides
And of course most of the desserts and snacks are vegetarian too.