Hi, The Sydney rate assessment books are online and can be a great people finder. There are 2 entries for a Jacob Whitfield, one in 1845 and one in 1852 both at Market Lane. http://www.cityofsydney.nsw.gov.au/assessmentbooks/
Would your Jacob have been a "notorious receiver of stolen goods"? The NLA are digitizing early newspapers, and there is a mention of a Jacob Whitfield in the Sydney Gazette - 3 October 1839 (page 2)and 8 Oct 1839 (page 2)http://ndpbeta.nla.gov.au/ndp/del/home
The Sydney Gazette has only been done to 1842 so far, with the Sydney Herald to follow (post 1842) So perhaps keep checking back for any mentions.
I have Police Gazettes 1862 - 1900, maybe a bit late for Jacob, but I had a look and only found William Whitfield of Picton whose stolen horse was recovered.
From experience, NSW indexes are not complete. I have found events in original registers that have not been indexed, and have no idea why. Also pre 1856, no body, no burial, so no record!! This is particularly so for marine deaths, and sometimes the only way to find them is through the newspapers. Finally, I would check out the James Whitfield who died in 1856 - you never know!