Doha is quite big on erotic massage, which is remarkable in a conservative Gulf state. The majority of the advertisers only accept appointments via WhatsApp, like Doha Body Massage (http://www.dohabodymassage.com/) or Qatar Massage 24 (https://www.qatarmassage24.com/). I got a hunch that they offer more than just a massage. Not that I mind, the Asian girls are hot and I doubt they’ll go further if you don’t want them to.
You can give Twitter posts like this one (https://twitter.com/doha_center?lang=en) or the classifieds a shot too. You might get lucky at the hotel spa’s but I wouldn’t count on too much. Royal Lady Spa (http://www.royalthailadyspa.com/) at Villa No.1 Al Waab Street, is one of the few actual studios in Doha. It might not be very erotic but nothing wrong with undergoing a great Thai massage experience.