Qantas didn't run Comets. They used BOAC aircraft, as was done for a number of other "Empire" carriers, at a time when jets were few and far between. They didn't have Britannias either; the one above just has a Qantas sticker applied.
However, the OP says that the aircraft had propellers, and being an Athens to Melbourne emigrant charter I would presume it was a Britannia 100, which were starting to get bumped from main scheduled BOAC runs by the jets. The Qantas/BOAC pool was still dominant and they got the pick of government-paid charters.
I too wondered if Austrian was an error for Australian, but equally can imagine an emigrant charter for a London-based aircraft filling up half in Vienna and the other half in Athens before heading onward. Incidentally, the engine intake icing issue principally afflicted the prototypes, and was pretty much dealt with when they finally entered service, which had been significantly delayed as a result. Shortage of spares downroute for the otherwise unknown Proteus engine was a much more likely issue.
If anyone has full sets of Propliner magazine, as a number of us here do (mine are too far back in the attic) there was detailed coverage of BOAC Britannia operations, including specific mentions of some notable charters they performed. That might be the best bet.