Hi Definetly u will get the qatari driving license hassle free within one hour after producing your saudi license ..
I recently got it ( I had kuwaiti license) ..

But they returned me my Kuwaiti license as well ..

That was the best part.

It will cost you 150 Qatari riyal
You will need NOC from your qatari sponser , two photographs and working credit or debit card(They wont accept cash)