As I know there are only CBSE schools in Doha. You can try Birla Public School, Delhi Public School, Doha Modern Indian school or MES indian school. I recently took admission in BPS for my kids in KG-I and Class-I. They were also in ICSE schools. But for the higher classes it will be little bit difficult to get admission. So better check the availability here before taking TC from there, bcos TC validity is one month. As your child is from ICSE there will be some wreitten test.
In my opinion better to wait till next yr starting as only 3 months r left after december.
thanks,