TC 'Alby' in April '78 was still classed as one if I remember correctly, and it ventured well to the South of Perth, as the following link will show...
Tropical Cyclone Alby
The plot shows it still classed as a cyclone passing 35S - the equivalent of Albany.
We had not long moved into our new house in the Perth suburb of Thornlie, 11nm in from the coast and had a neighbour's vintage Paperbark blown over - right across our power lines, and the power was off for over three days until the authority of the time could reconnect.
Lots of mostly 'minor' damage widespread.