My PT nanny (2 days a week, 8 hrs/day) started at $11 when my son was 4 months old but I increased her rate to $12 after interviewing another sitter for an extra day (which my sitter couldn't do) who was getting paid $12. This sitter had more experience but was just not someone I'd leave my child with. So, I figured my sitter deserved more.
It's now been almost a year with my sitter and I will likely raise her rate to $13. She deserves it. She's wonderful.
So, I guess I could say that in my experience between $11 and $15 is a good range. I would base it on experience and what you're asking her to do. Will she be making meals? Driving your child, etc.
Hope that helps!