Don't take this as gospel but I had the thing explained to me recently:

Get an International Driver's Licence a.s.a.p. It's valid for 3 weeks in Qatar (as opposed to 3 or 6 months elsewhere).

Within these 3 weeks, go to the Traffic Dept. in Madinat Khalifa and apply for a temporary Qatari licence. This is then valid for three months.

This was from a pretty knowledgeable source.

I am not sure if an Australian licence qualifies for exemption from the test. I think not because they seem to only exempt 1st world licences from countries that drive on the right side. Worth a shot though.

Good luck.

*** Light travels faster than sound. That's why most people appear bright until they open their mouths.