I am surprised she isn't setting the rate for you.
When my son was an infant and I checked into daycare centers, they were charging between 190-250 a week 3 years ago.
I took him instead to a woman who did daycare out of her home. She watched many other children as well but was not licensed. She had some experience and was older and had 2 grown children and she charged me 170.00 a week.... a great deal in this area! Since this woman is watching only your child though, you might consider more like a starting nanny pay (which I am not sure how much that is). I now have him (at almost 3) in a home daycare similar to a Montessori school and it is 200.00 a week.
So, I hope that gives you an idea. If you haven't looked into it, see if your school has a daycare spending account option where you can pay your daycare expenses pre tax.
Oh, and just to add, I too work at a school so the hours are comparable. I would expect the rates to be higher while they are infants, lower as they get older. Only reason mine increased is because I had such a deal at first and I chose to take him to a more expensive place because I thought it was worth it for his education and the wonderful environment there.