Thirteen minutes after departing Brisbane the crew was instructed to "contact Brisbane Control now on 127.2" (the next VHF en route radio frequency). This message was received at 1023 E.S.T. and acknowledged. At 1039 hours, Brisbane Flight Service received a radio check call from the aircraft on HF. However, despite numerous calls from Brisbane, Sydney, and Melbourne Airways Operations units, nothing further was heard from the aircraft on VHF until 1144 hours when the crew contacted Sydney Control requesting transfer instructions to Melbourne. The aircraft's progress was monitored on radar throughout the flight and, as it appeared to behaving normally, no fears were held for its safety. In his report, the Captain stated that both VHF radios had been inadvertently selected to 127.3 MHz instead of 127.2 MHz. Both pilots had heard aircraft communicating on this frequency, which is a Melbourne-Sydney route frequency, and believed communications were normal. Neither pilot could recall transfer instructions being issued, or calling Brisbane Control on frequency transfer. Examination of taped air/ground communications did not reveal any record of the crew having checked-in on frequency 127.3 MHz following transfer, as required by standard procedures.