It's apparent that money is no object, all they would need to have their own airport representation would be a couple of Duty Officers to cover seven days a week overseeing the handling agent and dealing face to face with passenger enquiries.
Check-in opens, what, three hours before and everything should be wrapped up by one hour after departure ... Wow, these staff are going to be working some seriously long hours!
Much easier and cost effective to provide the handling agent with some Qatar uniforms, the agent appoints their own dedicated Qatar check-in staff, then besides a couple of their own staff Qatar don't need to worry about hiring and firing etc.
But then that's too simple for the M. East!