It's faster if you just go to the police station and ask for a 'Good Conduct certificate'. That is what it is called here in Dubai. You can get it within one hour. By mail it can take upto 10 days.
I assume you are one of the EK Aussie crew who applied for V Australia? Good luck anyways!
Here is a link explaining the Police clearance certificates.
http://www.dubaipolice.gov.ae/dp/eng...&ArticalType=1