This is a good review of the lounge, but as most do, they have missed the extremities
Review: Qatar Airways Al Mourjan Business Class Lounge Doha Airport DOH - One Mile at a Time
The sleeping area is found just beyond the business centre. There is about 12 beds and they will bring blankets and pillows (sometimes you have to ask). Also, when you go down to the deli, you can turn right to go through to the toilets, a second lot of showers and a quiet room that is basically a sleeping room. If you turn left at the deli and go past the games room, you come to the family area which is about sectioned of areas for a family. The lounges are big enough to sleep on as well, but they will kick out people who are just there to sleep as it is for families.
I have found the wait times for the showers have blown out a huge amount (mainly because they are so good). We just went through 3 times and the shortest wait was 1.5 hours so get in early if you want to book it.