Hi
We just recently inported our dog from the UK. Also, there were no quarantine restrictions as long as all the terms stipulated have been fulfilled. The UK version of AVA was DEFRA and they gave us all the info we needed for the export and import requirements. Try and find out the equivaent in Australia for advise. We also used "Pet Movers" (petmovers.com.sg) here in Singapore who handled all the import documentation and dog license application (for a very reasonable cost). I would highly recommend using their services as it made the import completely stress free.
If your dog is on the same flight as you he will probably travel as cargo so you wont be collecting him in the baggage reclaim. If you appoint Pet Movers they will collect him from the Animal Customs Centre and deliver him to your home. Milo landed at 6am and he was here in our house at 9am, so it was fantastic.
Feel free to email me directly if you have any further questions..
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