As far as I can tell mobility scooter just have to apply to the relevant TGA as they are considered a medical device - or essentially a motorised wheelchair, so no one can sell, import or modify one beyond what is specified. That being said they are allowed on walking tracks that bicycles have been excluded from.
They don't need to be registered can be driven on the footpath, top speed is pretty slow 6-8kms tops, I see NSW legislation is 10km... that is flat knacker on a footpath with other people around! They can use bike lanes and paths, but anything on road, while not illegal his strongly discouraged.
On a side note your not allowed to be drunk when driving one, but also dont need a liscence.
The death toll from scooter accidents is massive! when you fall off one of these at 88, its the same as wrapping a car around a pole at 160...
Use to teach scooter use and safety at hospitals moblity clinic.
http://roadsafety.transport.nsw.gov.au/stayingsafe/pedestrians/motorisedwheelchairs/
My aims in old life is to do naked burnouts on the wet grass at the retire village I have been sentence too, go out with a bang, before I roll it in a garden bed and cark it.