QNIM, no it doesn't
CAR 166 (g)
after take-off, not alter heading from the take-off heading at a height at least 500 feet above terrain, if the alteration was not:
(i) directed by Air Traffic Control: or
(ii) necessary due to the terrain
Point (ii) is also very relevant most companies have Terrain Clearance Departures (TCD) at places like Hobart the 30 departure reads,
Maintain Runway Heading at 250 feet but not before Departure End of Runway, turn right xxxx