Riding on footpaths, by anyone not under 12 is currently illegal in WA (regulation 216)
BUT, the very interesting fact is that
virtually all footpaths, even when they are not signed, are shared paths, so that regulation does not apply unless the path is specifically signed as a footpath or to prohibit cycling.
The reason for this is in the Definitions at the front of the Road Traffic Code 2000. A shared path is defined as:
A shared path means an area open to the public (except a separated footpath) that is designated for, or has as one of its main uses, use by both the riders of bicycles and pedestrians,
The key part here is that a path does not have to be designed as, or intended to be, a shared path and does not need to be signed as such to meet that definition or to be one. In fact the very regulation that makes it an offence to ride on a footpath actually permits 'one of its main uses by riders of bicycles (albeit under 12 but the age is immaterial to the use). Thus, unless marked otherwise, most if not all footpaths actually meet the definition of, and therefore are, shared paths. Add to this the adult users that ride on most paths and that main use is compounded. If fact, when you watch someone cycling on any footpath in Perth CBD the police will generally move out of their way and not even blink.
So, the law doesn't even need changing as it already allows cycling on 'footpaths'. It just needs a clarification, some definition of what is safe, and publicity.
What is safe, the road code already specifies 10 km/h as the safe speed for footpaths, see motorised gophers and Australia Post motorcycles, so this could be the 'safe' speed for footpaths unless signed as a shared path in which case the normal design presumption shared path speed of 20km/h (Austroads) could apply unless signed otherwise.