Australia’s agriculture conditions for dogs:

• A dog can be taken to Australia, but only if it came from an approved country, is not pregnant and is not a banned breed or domestic/non-domestic hybrid.
• The dog must first be fully vaccinated and microchipped before it can get an import permit
• Within 45 days of travel it has to test clear for diseases including Ehrlichia canis, Leptospirosis, rabies and parasites
• Five days before travel it must be health-checked by a government-approved vet in the export country
• On arrival it must go into government quarantine for a minimum of 10 days on arrival, longer if it is seen as coming from a riskier country or it shows signs of ill-health
• Private jets are subject to the same regulations as any other vessel or aircraft

Source: Australian Department of Agriculture