Down here I know you can have a motor on a bike but it must be below 50CC. This is why it is common to buy the ebay 49cc bike engine (has 49cc cast into crankcase) and use the larger piston, barrel and carby.
Having said that it'd be poor form for a cop to give a young bloke a ticket for having some nostalgic style.
It's actually a power output limit, not engine capacity as such. Has to be 200W or less, to qualify as a legal 'power assisted bicycle'. And it's up to the rider to have proof of that. The rule in Queensland is that electric motors only are permitted; not as it is in Vic, where other motor types are OK up to the 200W total power limit.
This rule was brought in to stop those 50cc 'monkey bikes' being ridden on the street, so it
is enforced.
It would be expensive to get done, too - no rego, no third party, unroadworthy and no motorcycle licence...