Well, I've not dated one, I've liked one and got to know one. I have to say it's a bit of a different ballgame. They can be very cold in your initial interactions with you, but once they open up they're pretty cool. I think the whole "be yourself" thing is more applicable here, likely because you got AS might be the reason she's into you in the first place. It's a commonality. The girl I met I could relax around a good deal more than a normal girl. She might be looking for the same feeling.
I mean, there's not a lot of real advice you can get, as people are individuals and all. Pretty much you'll have to wait and see. I would say with a girl with AS, you probably have a better likelihood of "being yourself" actually working. Hell, that's how I met that girl actually. I played my Japanese music at the rink and she's like "L Arc En Ciel is my favorite band!" and that sparked things really. I'd talked to her a bit, but she was very guarded and I just assumed she hated me or something until I played L'Arc En Ciel. So in this case, "Be yourself" might actually work.
I dunno, maybe completely useless advice. I guess as far as things not to do, I guess don't ramble on forever. I'm kinda significantly more of a loser than you are, so yeah. As far as the girl I met, I concluded she was just as guarded and inept at romantic relationships as I am, it was sorta unsaid, but mutually understood that we both couldn't handle a relationship. It depends, Aspergers or not, the girl could be completely different than you, or she could be a female clone of you. If she's a female clone of you, "Do unto others..." might actually work?
Again, maybe totally useless.