The Cherokee departed from runway 14 to track to Flat Top Island, 4 NM east of Mackay, to carry out airwork. Soon after, a Brasilia reported ready to takeoff from the same runway, with the intention of tracking to Rockhampton via the 131 VOR radial. The aerodrome controller cleared the Brasilia to takeoff after observing the Cherokee appeared to be established on track to Flat Top Island. The pilot of the Brasilia reported that as he turned left to intercept the 131 VOR radial, he noticed the VOR had apparently failed, and attempted to resolve the problem. Soon after, the copilot reported another aircraft immediately ahead. The pilot saw a Cherokee about 200 metres away at the same altitude, but slightly to the left, and passing from left to right. He took immediate evasive action by turning left to pass behind the other aircraft. The investigation established that the instructor in the Cherokee had been concentrating on the instructional sequence, and had not continued on track to Flat Top Island as cleared. The Cherokee had been subsequently turned onto a southwesterly heading, which conflicted with the flight path of the departing Brasilia.