Originally Posted by lost_in_translation

Yes, this is possible and you should have plenty time to do this. Outside of rush hour the centre of Doha is not a long drive at all (but at rush hour things are somewhat different!). There is no good public transport connection to the airport so you'll be relying on Ubers, but they are cheap and efficient in Doha. My advice would be to head to Al Safwa and ask for a sleeping room on arrival, have a shower there and possibly take a quick nap, then enjoy a leisurely breakfast in Al Safwa afterwards until after rush hour has finished, before heading out in Doha around 9.30/10 for a few hours. If this is a weekend you'll have even less trouble and can leave earlier without issues. You don't need to be back at DOH until a couple of hours before your flight. The premium immigration and security at DOH is extremely efficient, I wouldn't recommend this but I've left the DoubleTree (about 15-20 minutes drive) around 1 hour 15 minutes before a long haul flight before and still managed to reach the gate comfortably before boarding commenced...