Wow.. I'm surprised with the comments, I've been to Qatar, doha twice for work and I punted about 4 times.
I agree it's not as easy as dubai, which has a massage parlour (or a brothel) every few roads recently (compared to dubai of 15 years ago) and online escorts.
So If your in Doha, I punted twice using Massage Republic, choice of 100s of beautiful girls (mainly oriental), This is a popular website, equivalent of Adultwork.
And I visited 2 x massage parlours where I got a massage and paid extra for a short sex session, bj and some oral, similar price to dubai. (£80-£100)..
If it helps I stayed once near Al Sadd metro and once near Al Mansoura station.
It's defenitly a Conservative country but I predict there trying to adapt like Dubai. In dubai you've got Arab men wearing that muslim long clothes things walking into the parlours openly.. I've reviewed one of them parlours..