OK, I wasn't satisfied with my answer so I did some looking on QL. (Couldn't find a darn thing in MOI.)

margaret07 said Qatar driving licence ...
"You need to apply for a licence with 7 days of arriving in Qatar. There is a form that needs to be signed by your sponsor giving you permission to drive. I had a Canadian licence, and was able to get a Qatari licence automatically with only an eye test. You will need 3 passport size photos.