Well sure. Should she? It depends.
As a community member and parent, I say ok. If your kid is well behaved, old enough to know their name/address/phone, knows not to talk to strangers, knows who to ask for help, etc, then, ok. My niece Caitlyn is 5, and I would say she is perfectly capable of spending 3 minutes alone in the picture book room without getting into trouble or being abducted.
Well, as a librarian, this bothers me.
We are not your babysitters. Nor are we your security guards. We do what we can, but we certainly can't watch out for everyone and everything all the time.
Even if there is no one else around for the librarian to help, there could be at any moment. The phone could ring, she could get called away. It's not fair to ask her to watch your child, and then get annoyed when she says that she can't be responsible, because it is, after all, a public place.
You wouldn't go into a supermarket and ask the cashier to watch your kid while you shop, right? Because she has work to do.
And watching your kid is not part of her job description.