Don't do anything in a hurry. A girl isn't like the last box of Fruit Loops on the shelf you have to grab before it's gone. For one thing, it's just as likely she IS dating someone now and maybe down the road she'd be available, so asking her too soon wouldn't work. For another, racing against the clock leads you to make poor decisions and say awkward things. Trust me, I know.
I'm curious how you got her email in the first place. Did she offer it to you, or did you ask her for it? If she offered it to you, then I see no problem in emailing her and asking to go out for coffee or something. If you asked her for it, or you looked it up, then I'd be more cautious, since she may only have given it to you out of politeness.
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Everything would be better if you were in charge.