Sleep'n'fly is an expensive (charged in USD) but convenient and reasonably comfortable way to pass the night for a long night's layover in Doha airport. My pod was not that easy to locate but efficient check-in once you do, and you can easily sleep for the duration of your reservation. My single bed room was the tiniest 'room' I've ever slept in but remains one of the most sensible travel decisions I have ever made.
They woke me even though I declined a wake-up call (was appreciated),  and I think a shower could be included for the price!
If they could determine which node of the airport you might be arriving in, or let you sleep at either end, that would be even better. Overall, much easier than getting into Doha with the risk of then missing your onward flight.