Attached is an image of a cover acquired by my father many, many moons ago. The letter was posted on 6 December 1934 (although the Brisbane date stamp doesn't show the year).
The inaugural flight left Brisbane on 10 December via QUANTAS for transport to Darwin where the mail would connect with Imperial Airways. It was intended that QUANTAS was to deliver to Imperial at Singapore but this was apparently associated with an airworthiness issue with QANTAS's DH Dragon Rapide planes.
Imperial then carried the mail with many, many stops to Brindisi in Italy where it was put on a train to Paris. It was then flown from Pais to Croydon Airport just outside London, reportedly arriving on schedule almost to the minute, on 24 December. Finally, believe it or not, the mail was delivered to destination by first post on Christmas day.
New Zealand was included in this scheme and their story is even more hair raising. Mail for the flight was sent by steamer (SS Monterey) from Aukland (30 November) to Sydney (3 December). The mail was sent by rail to Coonamundra on the night of 9-10 December, then by Butler Air Transport to Brisbane to connect with the flight to Darwin.
Two interesting sites are:
http://www.nzstamps.org.uk/air/exte.../austuk.htmland
http://www.airwaysmuseum.com/Qantas...ail%2034.htm