What is the law?
Australia to save time and effort effectively copied the exact same laws in Europe in regards to electric bikes. It is illegal to ride an electric bicycle on the road or on bike paths with a stated power output of more than 200w without the pedal assistance system, or 250w with a pedal assist system. It is incredibly hard to monitor and you may see ebikes on the road with up to 2000w motors.
Do I need a driving license?
If you’re riding an ebike that abides by the laws described above (EN15194) you are able to ride an electric bike without a driving license. If the bike is overpowered technically it will need to be registered as it is classified as a road vehicle and you would require a driving license.
Are there any other laws I need to be aware of?
A law that is enforced around Australia is that it is compulsory to wear a helmet and if caught not doing so may result in a fine. If the police officer is also having a really bad day he/she may also fine you for riding on the footpath. You also must have a rear and front light.