As per new system, you can not go and book any appointment with any doctor / clinics in Hamad Hospital.
You have to go to your local health centre and get a referral and than go to Clinic / doctor at Hamad Hospital. They will submit the referrel and will call you back with in week or so time.

I requested the same and the nearest available appointment they gave me for ENT Clinic (evennig shift) is March 2013.

Hope this will help.