After making the necessary radio calls and arranging separation with an inbound aircraft, VH-LNB taxied for take-off from runway 19. While taxiing the crew were busy completing the pre-takeoff checklist and giving a safety briefing to the passengers on the aircraft public address system. The pilot of another aircraft, VH-DRG, made a radio call to advise VH-LNB that he was inbound to Port Lincoln. There was no response from the crew of VH-LNB. After takeoff, when established in a turn to the left, the crew of VH-LNB observed VH-DRG pass from left to right in front of and about 80 ft below their aircraft. The pilot of VH-DRG stated that communications with all other aircraft had been satisfactory. When the departing aircraft had not responded to his transmission he kept a lookout and first sighted VH-LNB when it was about 500 metres away. He turned his aircraft away but the other aircraft turned towards him and he was unable to avoid the aircraft coming into close proximity with each other.