I'm a father of three, so for your question, I tried to imagine what I might have done had I been your place.
I believe I would be open about it, actually. You may not always get the responses you'd prefer, but by being open about things from the start, your daughter will never get the impression her AS is something shameful that needs to be hidden (and you did say she "picks up on everything"). For every person who might be put off or discriminate against her, there will be others who will gladly understand her better for it. As I see it, the more people who understand a bit about AS, from real-life examples, the better the world will be for your little girl in the future.
I agree with Spinning Compass that the worst way to inform someone new would be whilst your daughter is in meltdown mode. I had a woman apologise to me in an airport once, as her son with ADHD was having a tantrum. She looked tired and harried when she told me why he was acting as he was, and I admit, that scene has stayed with me with "This is ADHD" as a caption. But if you mentioned your girl's AS casually, at another time, as though it's no big deal, she can make a positive impression that may help educate a mind or two. For your part, though, you would want to make sure you're well-versed enough about AS to be a good advocate for her. If people ask questions, you'll need at least a few answers or the opportunity will be lost.