Between 6:00am and noon, the airport is not busy, and the taxi line shouldn't be too long, but I agree with meFIRST -- the city is remarkably slow at that time of day. One area that I'd recommend seeing on a stop-over is souq waqif, but that will be pretty much closed in the morning.

In my opinion, the premium terminals are not much to write home about. The food is nothing special and there are few reading materials. There is the "spa" on the first-class side (and a shower on the business-class side), but there is no place to recline and sleep, as there is in the main terminal at the airport.

If you can spare the $28 (I think that you would need a separate visa for each stopover), then I would at least kill an 1-1.5 hours by taking a taxi on a loop through the city -- maybe go to the Ritz-Carlton, which is across town, for breakfast, the walk around the Pearl, the man-made island, although I believe that as of this moment, little will be open in the morning.