You can
qoute from "http://www.qatarliving.com/cars-0/wiki/drivers-license"

Within the week a temporary drivers license can be obtained from the Madina Khalifa Traffic Department that would be valid for the duration of your visa.

The requirements are:

• A completed application form in Arabic or English
• Original license from country of origin
• ID
• Passport
• Copy Of Passport
• Three Passport Size Photos.
• An eye test