The family moved to Melbourne, Victoria in 1852, and the young Wilkinson was educated at a private school conducted by the Rev.
In December 1859 Wilkinson was given a position in the Geological Survey of Victoria under Alfred Richard Cecil Selwyn.
In 1863 he was sent to explore the Cape Otway (Victoria) region and in 1866 succeeded Daintree when the latter left for Queensland.
Wilkinson was respected by his colleagues, who did good work in connexion with the mining industry, and was the first to suggest to the government the possibility of finding subterranean water in western New South Wales.
The fine collection of minerals in the Sydney geological survey museum was founded and largely brought together by him.