I believe these gold deposits would be discovered fairly quickly, it only took like 15 years after the first settlement in Melbourne for these gold deposits to be discovered. If a settlement in OTL was established around 1805 (which is very possible*) then by about roughly 1815 these gold deposits would be discovered.
*In 1803 an unsuccessful British settlement was established in the region where OTL Melbourne is, however they chose a place in the region where the soils were poor. It took until 1835 a settlement was established in a region with one the best soils in Australia was established. The discovery of these gold deposits say in 1820 would make an interesting timeline in it's own right by it's self.
*The discovery of gold in OTL Central Victoria was in 1851, that triggered a gold rush comparable to that of California.