Congratulations! What an adorable dog. How exciting to have a new best friend!

I don't know about the anxiety thing, my shelter dog has never had any separation anxiety (although she did eat like a pig for the first couple of weeks after I brought her home). My pure-bred from a breeder-dog (aka spoiled, never had a hard day in her life-dog), had severe separation anxiety. I couldn't leave her in the kitchen to go take a shower without her wailing like she was being tortured. She'd never been alone in her entire (7 week) life up until that point. I think shelter dogs can often be more well adjusted due to their life circumstances.

Either way, have fun. There may be a few rough spots at first, but they'll smooth out and you'll have many happy joy-filled years together.