1st up, WA is a minefield of overlapping jurisdictions.
2nd, you cannot prospect in state forest & national parks. Period. (Unless you are a huge mining company with loads of $$ to throw around), & this includes all rivers & streams within them. If you are within a water catchment area, WaterCorp will
oop: on you.
3rdly, there is not much gold in the rivers anyway. ie, SFA.
. The Boddington gold mine is the only real gold area outside the regular inland goldfields, that is close to any river that runs anywhere near Perth. (there are small deposits outside Donnybrook, all state forest, NP, & private property. 1 guy does actually have a SPL down there)
If you are really keen, your best bet is to identify a likely area on private farmland, & OBTAIN THE FARMERS PERMISSION. Despite what the prospecting rules may say, if you trespass, farmers have been known to go hunting vermin, where you may happen to be. Very unpleasant altercations then occur.
Sorry to blow your idea away, but many have contemplated your idea before.