I was never fond of babysitting as a routine source of income as a teen. I never set a rate specifically, but back then, where I lived, $5/hr was considered really good. Most people paid would pay $3-$4, but some thought $1-$2 was enough. When I did babysit I quickly learned which jobs to take and which to decline. When I was old enough, I got a job waitress. The hourly rate was low but the tips put me over $10/hr most days.
If your neighbors do pay her more, then you have a supply/demand/local economy situation that should be considered by both parties.
You're not being 'ripped off' in any case. You're simply having to decide if this particular sitter is worth $11/hr to you. She offers a service, you get to choose to use it or not. At the same time, you're not 'taking advantage' of her, as she is not obligated to babysit for you at all. (At 17, I wouldn't have canceled a date to babysit, so I think that is odd that she'd even consider it. I'd just tell you I was busy.)
What a teen might make at McD's is not relevant to the situation as you are not McDs and she doesn't work there. The important data is what you pay, what your neighbors pay, what she charges and what other sitters in your area charge. If you talk to neighbors and other sitters, it might help you to come to a decision.