Eliza--as said above housing won't be a problem to find, but schools are another matter.

Have you visited Doha? I know it's a pain but a six-hour flight will put you here for the weekend and the experience will likely alleviate many of your fears. I lot of companies offer this as part of their recruitment packages. You could also make appoints with the schools for tours--they're more likely to take the time to see you if you are visiting.

You may have to be in a less-than-ideal school next year, but try Compass, Sherborne, British Montessorie, and Park House. DESS is arguably the best for what you are looking for followed by Doha College, but both of these will be full. Call anyway, because for older years its sometimes easier to locate places. However, to get into these two find out the earliest day that they take applications for the following school year (some time in Oct./Nov.) and make sure you submit your application at the start of THAT DAY. We did this and had no trouble landing a preschool spot for our son--no older siblings in the school but he does have a British passport.

Also, Doha Moms is a good group to make initial contacts and friends.

Good luck!