You may apply for temporary driver's license if you sponsor issues you with a noc. You take this certificate, go to Madina Khalifa along with your original drivers license (not all drivers licenses are accepted, I'm afraid), a picture with blue/red background and a copy of your passport. It'll cost you QR180 that can only be paid via credit/debit card. You'll have to undergo an eye test over there and they'll convert it for you on the spot. It'll only be valid for 3 months from the date of entry in to Qatar.
After you get your RP then you just take your temporary license and another letter from the company (though I have read that this noc now is no longer needed - when I got mine 2 months ago it was still needed), another QR250 and you've got your permanent license.