This is just my 2 cents but when I worked at my kids preschool last year watching 8 one year olds, I got paid $9 an hour. It was alot of back breaking work along with changing diapers.
Plus, at 13 and having not been a babysitter before, there will probably be some things she will have to learn "on the job." I have used a new babysitter before and she had alot to learn. I liked her and still use her and she's really great now. But I definitely had to spell things out for her a little more than for someone who's done it for a while.
It's my opinion she ought to ask for $7.50 - $8.00 an hour. The kids she'll be watching are going to be very self sufficient. The younger the kids and the more experience she gets she could start upping her price.
Just my opinion.