Hello there.
I was looking for a very reliable and good hairdresser in Doha too - and my friend recommended Hecham at Spa Chakra - which is opposite City Centre, in the Al Fardan Towers.
He cut my hair last Friday and I'm very very happy - he's fantastic and professional and it was like being back in the UK!
I would recommend you call and see Hecham or Eric (my friend saw him and her hair looks amazing!).
All the best. Spa Chakra is on - 499 9250.