You should try DESS (Doha English Speaking School), Doha College. Those are definetely the best schools following the british curriculum.
If you can't get a space immediately you can get your kids into Cedars Tutoring Center. It's a bridging school for those kids on waiting lists. You should find the homepages of all three schools in the internet. There you get all necessary informations reg. tuition fees etc.

Finding an appartment should also be possible. Check classifieds on gulf-times.com

Good Luck!