Call 180 (Qtel Hotline) and ask for Phone Number of Moror (Police, Traffic Department).

As you are Australian, maybe you will be able to replace your australian license by a qatari one otherwise you have to do a test at a driving school (in case you fail, you have to undergo a driving class)

In both cases , you will need the following :

1. A letter from your sponsor.
2. Eyes Test (most opticians do the eye test for Driving License)
3. Photocopy of your Qatari ID
4. Photos - 2 or 3 Numbers

The fees for getting the license are 200 or 250 paid by CARD (cash not allowed)