Nice bike there Joe, and it does bring back some memories.
Malvern Star was perhaps the biggest manuf. of push bikes
and motor bikes in Melb., in the 1930-60 period.
The model you have pic there was known as an Auto Bike,
and were available in various colors with red most common.
They were based on British bikes of the period, such as
Raleigh, BSA etc., and most invariably used Villiers motors.

Their heyday was the 1940s and 50s, and by the 60s no one
wanted them. They were literally thrown out.

Does anyone remember the Velo-Solex?
Motor about 50cc, mounted above front wheel driving
a friction roller direct to the tire.
No need for a chain or gearbox, but the tire wore out in no time.