Hi guys, what are our options when faced with an 8hr 10mins overnight connection at Doha?
Two adults.
Arriving from BKK into Doha at 23:55 in first class; departing for Birmingham BHX at 08:05 in business class.
Body clock will be telling me the time is almost 4am when we land in Doha.

Happy to read an article if one exists if anyone could kindly link it.
Otherwise, would be good to understand the likelihood of getting a bed or two in Al Safwa (are we even allowed in since we only flew in on first class, not departing), or if Qatar are able to put us in the airport hotel (I asked on the phone but the agent didn't seem to understand and said I should pick an earlier departing flight (there isn't one to BHX)).
If no complimentary beds are available, should I look to book an airport hotel? (which one?)

Any advice or links to existing articles greatly appreciated.
Thanks.

EDIT: asked QR customer services again. Their view is that because there is a flight that departs BKK at 02:30, and which has a far shorter connection than the 21:00 departure from BKK I am interested in, no complimentary accommodation is available.
I pointed out that any normal person would head off to the airport on the night before, in order to get to the airport 2.5hrs - 3hrs ahead of departure time and that I specifically want to depart in the evening that day as I have stuff to get on with before heading to BKK airport.
They are correct on a technicality I guess, but it feels wrong.