Most of us don't even realize there is a game or a dance until we are much older, so no wonder we never learned the steps properly. You are not dealing with a savvy dater. While she may like you and let you know in no uncertain terms, she might not have a clue that you like her. But regardless, I do think it is important to take it slow.
Even the most self-aware Aspergirls, who face their challenges head on, still have sensory issues, social limits, high intelligence with unexpected cognitive deficits-there are all these things that will challenge you in your ideas of what a woman should be, what she can be and what she is.
If the time is right for a first date, make it clear where you will be going, whether it is dinner or drinks, what people wear in this place, even what the weather will be. It is probably best if you take the reins since she might have enough anxiety to deal with, without also having to choose the setting. Or, give her a couple options to pick from, not a Chinese menu of a hundred choices. And let it be just the two of you, unless you have mutual friends that she would like to invite.
Never ever use an Aspergirl for sex. Apparently some NT women are okay having purely sexual relationships. I do not think this is common for Asperger females. Not at all. We like our routines too much to have "casual sex" with different partners on a regular basis. And there would be too many adjustments to make.