I tried the calculator, and kids are getting much more than 7.75/hour. I think the going rate is about 10/highschool sitter. It really does depend on your neighborhood though. We are in a pretty wealthy area, but our neighborhood isn't that wealthy. We haven't had sitters here yet, but we have heard the same "pay what you think" when we ask.
As a late high school/college student with 5-7 years experience, I got about $5 for 3 kids an hour. This was just a few years ago! Wait that was over 10 years ago.
I think most of our friends pay somewhere around 7-10/hour a little north of Dallas. We mostly use family or trade outs with friends. That doesn't help your daughter, but it may help others. We had some friend ssit the other night, and we fed everyone (ourselves included) a really nice meal before we left. It was great for us because dinner cost us a whole $24 to feed 5 adults and one child (another friend came over to keep the others company). My hubby and I would have spent way more than that for dinner for ourselves and for a sitter. We were then able to go out (Blue Man Group concert), feel good about who was at our house, and know that we had saved a little money.