Like the PMs car, the number plate is put on the car that the G or PM is riding in, like the Airforce 1 call sign in the US. I have seen one of the cars the PM uses when he is over here has a PT number plate but it changes to the C*1 when he alights the vehicle.
Now who knows about the 1WA number plate? Who uses these? I know it is a government department but I think it is more likely MPs maybe Dept of Premier and Cabinet? Is there a difference between the 1WA and 9WA number plates you see at Parliament House?
The '1WA xxx' series were originally allocated to the Department of Premier and Cabinet for state government ministerial vehicles, though these days the ministerial cars just have standard issue plates. The 1WAs and 9WAs are generally now used on State Government fleet vehicles allocated to the Department of Premier and Cabinet, usually driven by public servants who have a vehicle as part of their package.
The Governor's vehicle probably has a conventional licence plate allocated to it, as it's a registered road-going vehicle with CTP insurance: I expect has an exemption from actually having to display it.