YES, YOU CAN....

I TOO HAVE A DRIVING LICENSE BASED ON VISIT VISA. YOU CAN OPT ANY OF TWO COURSE, SHORT COURSE OF 14 DAYS OR FULL COURSE OF 25/40 DAYS. IF YOU OPT SHORT COURSE YOU SHOULD HAVE A DRIVING LICESE OF YOUR HOME COUNTRY, WHICH SHOULD BE APPOVED BY TRAFFIC DEPT OF QATAR. YOU NEED TO HAVE THE FOLLOWING DOCS

AN NOC FROM THE ONE WHO GOT YOUR VISIT VISA ISSUED
A FORM TO BE FILLED FROM DRIVING SCHOOL
COPY OF YOUR VISIT VISA
COPY OF YOUR PASSPORT
3 PHOTOGRAPHS

IF YOU GET LICENSE, IT WILL BE VALID TILL THE DATE OF VALIDITY OF YOUR VISIT VISA.