depends on the insurer, Qatar Insurance Company said this in email to me

Thank you for your email! With regards to your query below, a foreigner is valid to drive in Doha with the following conditions:
Foreign driver with his country valid driving license allowed driving only for one week from entry date
Foreign driver with international valid driving license allowed driving for 6 months from entry date
Foreign driver with GCC driving license allowed driving for 3 months from entry date

As an Aussie your driving licence should be transferable to a Qatar one with only the eyetest (temporary, then permanent once RP sorted).