Australia has international airports that are serviced by flights from Asia, Europe and the Americas located in every state except Tasmania.
Airlines that provide services to and from these airports include (in no particular order):
Qantas Airways
Air Canada
British Airways
Malaysia Airlines
Cathay Pacific
United Airlines
Singapore Airlines
Air France
Air New Zealand
Thai Airways International
Emirates
Royal Brunei Airlines
JAL
Garuda Indonesia
Korean Air
Virgin Atlantic
Within Australia, there are two principal airlines and a number of others that provide a network to get you just about anywhere.
Qantas Airways
Virgin Blue
Tips for Booking Flights
For the best international fares, contact a travel agent. Dealing with the airlines directly does not always provide the best fares.
Avoid really cheap airfares that may have either unreasonable conditions or have extensive stopovers in connecting ports.
Try to avoid buying one way fares - these are usually almost as expensive as the return deals, and most likely you will be able to use the return flight to either return home, or at least visit home for a vacation.
It is also advisable to either ask your new employer (or your Latitudes Consultant) about what the employer's policy is regarding reimbursement of expenses incurred during relocation to Australia.