Would you charge more or less to babysit overnight?

I babysit a friend’s two young children a few afternoons a week. She normally pays me $12 an hour. This weekend she has to travel to a funeral and has asked if I can keep the kids overnight and what I would charge. Should I tell her the usual rate, or more since it’s overnight? Less because they’re sleeping? But here’s the thing, the kids sleep with their mom at home and the little one still wakes up for cups of milk several times a night and cries and cries if she doesn’t get it. Then I feel like a jerk for even charging her when she’s off to a funeral. What would you do?