Doohan and his father, five-time world champion Mick Doohan, are scheduled to take to the Albert Park circuit on three occasions as part of the Formula 1 Australian Grand Prix support programme.
It is the first time the pair had been on track together, with Doohan Jnr initially at the wheel of an F1 machine driven by Giancarlo Fisichella and Alex Wurz during the 2000 season and Doohan Snr, meanwhile, rode a production MotoGP Honda RCV213.
However, as their session ended, the Benetton began to emit an ominous plume of smoke.
A gearbox issue in the car has been enough to sideline it, with Doohan Jnr instead piloting a Brabham BT23B.
A 1960s spec formula racer, it had a limited run in Formula 1 in the hands of privateer Paul Seitz in 1969, alongside a number of non-championship outings in 1967 and 1968.
Doohan Jnr took the wheel of the historic racer for the day’s second outing, held shortly before Formula 1 qualifying, with his father again joining him on track.
A third outing is scheduled for Sunday at 13:35 AEDT.