perfect place to post this question. yes there are many private and government institutes for autistic kids.

ill name the few for u
1. qatar autism centre for special need www.qacsn.com
2. Step by step www.stepbystepqatar.com.
3. omega www.omegaqatar.com.
4. Doha centre for special need
5. the learning centre
6. shafullaha www.shafallah.org.qa/
7. sunbeam

almost every kind of therpy is avialable . The fee per month ranges from QAR 3000 upto QAR 5000 per month.

in case u need more information lemme know :-)