The Boeing 767 crew requested departure from Perth via a scenic flight along the Swan River. Air Traffic Control (ATC) advised the crew to expect approval for this modified departure track. Due to traffic and noise abatement requirements, the aircraft was initially cleared to maintain runway heading after take off. The crew acknowledged the clearance. The aircraft was seen to commence a right turn, at 1600 ft, after takeoff, conflicting with traffic departing off another runway. Shortly after ATC queried the crew's actions, the aircraft was seen to return to runway heading. By the time runway heading was regained, the aircraft had reached 2500 feet and was subsequently cleared to track via the Swan River. Although separation reduced to below the minimum required, there was no danger of collision due to the horizontal displacement, between the aircraft, and the high rate of climb of the Boeing 767.