There is a somewhat detailed tree on Ancestry showing that is name was Richard Burcham Hardy b.14/12/1817, bp.5/4/1818 City of London. Having checked on IGI this was at St. James Garlickhithe, London - son of James and Mary. Another son Henry Stuart Hardy b.12/5/1814, bp.29/5/1814 same place.
Marriage records show a James Hardy married Mary Palmer 20/2/1812 St. James Garlickhithe, London.
He was transported on the Charles Kerr 6/6/1837 having been convicted on 19/9/1836 Old Bailey, London. There's a quite lengthy note attached - when he arrived in Australia he and 3 other convicts (all named) were assigned to a W. E. Cormack of Williams River, Dungog. Various physical details are given.
Two separate people spoke up for him at his trial - he lived in the Bethnal Green area of London. One person was a weaver from Bethnal Green, the other was his father's employer who offered Richard a job if he was able to serve a custodial sentence rather than transportation. His fathers employer being a James Watson, Cabinet Maker and Timber Merchant of Bethnal Green Road. Richard Hardy at his trial said to be a cabinet maker for 3 1/2 yrs.
How accurate this is I can't say but reading through it all it does seems quite thorough. I wouldn't have thought he'd have been much older (regardless of the gravestone) because his youngest Ada was born 1871!!! If he'd been born c.1797 he'd have been 73/74 when she was conceived. I doubt that very much. There's also a picture of him and his wife although it's not dated.
Certainly, the arrival in Australia 1837 and his assignment to someone in Dungog all fits.
Annette