Here is my experience from today. Mrs. SoD and yours truly flew DOH-BEY on QR. We had four hours to make our BEY-DWC flight with FlyDubai (separate tickets). We tried to go through passport control to pick up a single piece of checked luggage. Passport control told us 'no, you have to go to the transit/transfer desk'. So, we leave the line and go to the transit/desk which is staffed by three people. We tell them our travel plans and they have a gentleman take our passports and the checked luggage tag from the QR flight. The gentleman tells us that it will be over an hour before the FlyDubai counter would be open so he escorts us up to the duty free area and welcomes us to go for a coffee/walk around as it beats sitting in the chairs by the transit counter. An hour and a half later, he finds us and hands us our passports back along with our FlyDubai boarding passes and the new FlyDubai checked luggage ticket. All done and very professional! We could not have been more pleased. ^^^
Additional note: I asked what hours the transit/transfer desk was staffed and they told me 24 hours a day. ^