The American School, Compass, Park House and Doha Montessori (not a Montessori school, despite the name), Sherborne and Int'l School of London are likely to be your top choices.

A UK passport is pretty much required for DESS, and I am assuming that it is for Doha College as well - but you'll want to verify this first. DESS is less expensive than many of the expat schools, but I don't know if Doha College follows suit or not.

Finding slots in school is not easy, and is likely to require some diligence on your part. I would bite the bullet on the phone bill rather than just relying on email.