In college we had a spherical geometry question on a final exam. It went something like that: If a trip is flown from Phoenix to Melbourne, calculate the Great Circle departure heading from Phoenix and arrival heading at Melbourne. As I recall, the departure heading from Phoenix was a little south of south-west.
Here is a route taken by Qantas flight 8 from Dallas/Fort Worth to Sydney:
http://flightaware.com/live/flight/QFA8/history/20170124/0205Z/KDFW/YSSY
While this route is not exactly Great Circle, it is close enough, also Dallas is further east than Phoenix so the initial heading would be somewhat more southerly than that from Phoenix.