Some schools do have buses (for an extra fee), the problem is with the timings - I've seen kids out as early as 0530 hrs waiting for their bus (and school doesn't actually start until 0700 or 0730 hrs). However, they seem to be mainly Arab or Asian children - so I assume they are attending Arab or Asian schools.

You need to get your kids' on the waiting lists for your preferred schools now as the better schools that have the American and British Curriculum are very popular with those expat (and other) communities.

Try expatwoman dot com for some more contacts and ideas (they have a list of schools and various items of interest to people new to Qatar)