If you have a Qatari Residence Permit you must have a Qatari driving license. If you have a Qatari RP and drive using a international driving license you are driving illegally.
You can get a Temporary driving license that allows you to drive for 6 months:

Temporary Driving License

The following items are required for a Temporary Driver's license (TDL):

a) Original driver’s license from home country.

b) Eye examination.

c) Process fees QR156.

d) Four personal photos.

e) Copy of Passport

Permanent Driver’s License

Converting the Temporary Driver's License to a Permanent Driver's License requires the following:

a) Temporary Driver’s License.

b) Two photos.

c) Copy of Passport and Residence Permit.

d) Process fees of QR156.