wow, babysitting is much cheaper here. I pay my sitter typically $5/hr for my two kids. I want someone that is more interested in my kids then the money. That said, for one kid if you're breaking it down by the hour I'd say $5-10/hr(since she'll have to feed all meals and all the extras). Unless he's one that wakes up much, then you might want to pay more for dealing with the middle of the night work.
We just had a sitter help us at nap time during a wedding and then later in the evening. She watched a total of 7hrs and we gave her $100. She thought it was an incredible pay, and it was worth it to us. We gave her more though because she did dress changes, and brought the kids from hotel to hall..she really went all out. Good luck, that's a hard rate to determine. If she's the type that is going to play with them all day and keep them occupied, I'd pay more. If she's going to sit on her butt and text her friends all day/night I'd pay less, (actually I wouldn't use her then). :)