I would book at room at the Oryx Rotana, which is literally only a three minute walk from the premium departure terminal. You should be good to leave the hotel at 6.15-6.30 and still make your flight and pay for your room in advance so that there is nothing to do on departure other than leave the room's key card at reception.

Your bags should stay in transit so all you will need to do is go straight through immigration, into a taxi and onwards to the hotel. I would not bother with the Al Maha services if you are travelling in business class, but look for the business class fast track and you should be in Qatar in no time at all.

All the above assumes that you are eligible for visa on arrival.