Well, one positive point of Facebook is that it's a way to ensure that the only people your child is talking to are people she knows. Her friends from school, etc. And if you insist that she secures her facebook page, then only they can see her updates and it protects her from some of the dangerous elements that could be lurking out there.
That said, yes there are dangers and uncertainties. But she is going to face those dangers at one point in her life anyway. The question here is, can she handle it?
In the case of my cousin, who is the same age as your daughter, she proved that she is not mature enough to handle a Facebook account. Particularly when she tried to arrange an "encounter" with a mentally challenged nineteen year-old.
In the end, it's her display of common sense that should tell you if she should get a Facebook account. If you can leave her alone at home without worrying about it, I'd say let her have the account. And at least if it's on your computer, you can more easily monitor who she is and isn't talking to.
The only thing you're doing by forbidding her to get one in the safety of your home is giving her the doorway to go to her friends' places and set it up there. (And lets not be naive about this. It is the biological imperative of all twelve year-olds to sneak past their parents.)