I have an International Drivers Licence that I used here - you can drive straight away with it without any other tests. Just remember to carry your Australian Drivers Licence with your International Licence. The International Licence is valid for 6 months in Qatar (as confirmed to me by the police after we got smashed into!).
You should probably swap over to a Qatari licence as soon as you can, and I don't think you need any other tests for this either, just your resicents card & Australian licence.
Not sure on the motorbikes though!