Sleepover birthday parties seem to start at 8 (2nd grade) at our DD's school. Generally the guests have been to the host's house before, though. And as the birthday girl's parent, I feel more comfortable with overnight guests if they've been to our house before and I know they are OK with our dog and are good guests. So I don't think being the "new" girl is a problem.
As for what to do.... we've had a some sort of activity for the girls to do when they arrive. Other than that, they pretty much entertain themselves. Dinner can be pizza, taco bar, etc. One year the girls decorated their own cupcakes. If the weather's nice, make outdoor games and activities available.