There are a lot of Austin posts already that cover the many places to eat:http://lazysmurf.wordpress.com/austin-sxsw-vegan-guide/http://lazysmurf.wordpress.com/a-vegan-tour-of-austin/
I think an Arlo's bacon cheeseburger, Bouldin Creek tofu scramble, a Vegan Nom 3 Amigos taco, a sundae from Sweet Relief, and a Wheatsville popcorn tofu pizza seem like the must haves to me.
Bangers is a great new bar with the most beer on tap in town (103) and they have a little dog area. Their menu doesn't look vegan friendly, but one of the veggie sausages is vegan and it is awesome. All the bread except pretzel is vegan there too.
Since I live here and don't have a dog I don't have much more advice about lodging or dogs, but good luck.