I know there's other threads on this as well, but I didn't see them. Your quote seems on the high side, but not unrealistic, I think. Especially considering they're licensed and insured. We pay $70 every other week and have a 1900 square foot house, though she doesn't clean our third floor since we're under renovation. I'm not even sure I'd ask her to do those rooms once we're finished because we won't be using most of the space. I think we have an awesome rate and I love, love, love our woman. She's been with us over two years now and I consider her like family.
It's probably not a bad idea to get some other quotes but how you feel about someone is equally important. You're having people in your house so you need to trust them (whether you're there or not) and like them IMO.
Hiring a cleaning person was the best thing we could have done for our marriage and our home lives, congrats on making that step!