Yes there is American School of Doha. One of the best school here.

Qatar is not as strict as Saudi ... lady can go out alone and can drive. Dress code i find it very relaxing. You can wear anything you want. As far as you not wearing skimpy skirt and top in the public, otherwise you will get stare by opposite sex. I normally out doing groceries shopping and school run with knee length skirt or jeans, with short sleeve top. You can wear a bit more revealing clothing when you go out to people's house or hotel.

We love it here ... hubby have plenty of hours to spend with the family. Very laid back lifestyle and very friendly expat community.

Good luck with your moving.