In the moi.gov.qa its showing the fee for dual RP is Qr 2000.
So it is possible. I am sorry I dont know the procedures.

"Allowing residence permit in Qatar along with a residence permit in any one of the GCC countries (Dual residence permit). QR 500 QR per year for students.
QR 2000 per year for organizations and companies. "

http://www.moi.gov.qa/site/english/deptFees/index1.html