here. Check out www.dohahomeeducators.com

The Learning Center is for grades 1-12 where children are of average or above average intelligence with learning difficulties. I suppose autism doesn't apply there, but check it out anyways.
www.tlc.edu.qa

Sunbeam Kindergarten info can be found at
sunbeamsqatar.com I've heard good and bad about it.

The shafallah Center is a brand new, state of the art, purpose built facility catering to serious special needs children.
Unfortunately what I have heard is that only Qatari or selected Arab children are allowed in.

Good luck with your search. There are not enough schools here for the population, so they can be very picky on who they let in. They have never needed to offer special services to get full enrollment and so it ends up being a neglected segment of Doha society.