Huh, Oryx website is showing booked up through the 5th of September. Wonder if it's a site bug or transit through there has gone parabolic? Guessing transit traffic. I know showing up at the Oryx desk on arrival is 99.9% guaranteed to fail, but I've never seen them booked out so far and i stay there several times per month.

I always book a room (weeks/months) in advance if it's an 8+ hour layover because comfortable rest is critical for the immune system and for overall physical and emotional health. To each his own, some like to power through 36 hours of travel.

As Schwann noted with accurate caveats, that sleeping area is an option however my wife tried it one time a few years ago on our first transit of DOH and no peace due to screaming babies/loud families. Plus, there is now frequently a wait to get one of the communal sleeping chairs.

12+ hour layover getting outside of the airport is an option if you carefully line up the necessary requirements. Personally, I would not try that on <12 hour layover, too much hassle.

If you are flying QSuites, that opens the possibility to time your sleep cycle to coincide with the sweet, sweet suite experience. Especially as QR does dine-on-demand (in J, I don't know about back cabin).