Please don't overlook that Richard COOPER who was also known as Thomas WALKER. Afterall, whenever any of us do find any reference to a Thomas Walker in the Queanbeyan district we need to remember there were at least two chaps in the 1830s, 1840s known by that name in that district...
Queanbeyan - that was and is the County of Murray.
The road from Sydney down through Queanbeyan - that road went through Cobbitty far earlier than the sub-divisions of land in the 1840s... Back before the Rum Rebellion of 1808 even ..... it was surveyed by various of Sir Thomas MITCHELL's teams in the early 1830s
One of my ancestors was one of the surveyors in his office, and in the field too. You will find many of the locality names are attributed to Thomas Mitchell. He often set about trying to find Anglo spelling for the local Tribal names of various geographical features...
National Library, Canberra
Do not buy the NSW BDM Early Church Record. Consider that there may well be better details available from the records held by the NLA, in Canberra.
https://catalogue.nla.gov.au/Record/74208 Records of the parish of Narellan, 1827-1927 / compiled by A.F. Pain
https://catalogue.nla.gov.au/Record/3540079 It is very possible that the chap at Cobbitty is not NOT our OPs chap, but I do think we need to check and see if the record does have any info that will help clarify this quest.
Any sightings from mid 1851 until closer to 1900 are going to be very difficult to sort, as the inflow of people once gold was discovered simply overwhelms any search for a former convict in NSW records unless there's known oral history, or confirmed family Bible entries, or written correspondence with signatures to check or identifying details in the correspondence... eg "I arrived in Sydney on ...th of ...... in the year 18..... on the ship ............ captain ............ and I married ........... the daughter/son of .............., a merchant/ag lab living at ............. I was born ......... at ......... my father was .......... / or another example 'I sold my land at ........ to ......... who arrived on the ship ........... in ..........." or 'I am not Joe Blow who arrived on the ........... under a bond. I am Joe Blow who arrived on the ........... on the ....th of ...... in 18xx with my wife, (her name) and children...... (name and ages)..' .
JM