Legally, you have to pay overtime. That is why banking hours is illegal, too. OT law is OT law. Which is why I would likely say "no" to this scenario.
But I agree with the above poster. I would only agree if a) I actually needed help that day, b) she could still do her full week without collapsing from exhaustion, and c) it wasn't going to cost me extra.
Otherwise, you might as well just pay her for another vacation day, since OT means you'd be paying for half a day already.