Hi Sandra
His Birth registration appears to be:
John Henry HAND - Sep Qtr 1856 Melton Mowbray (covers Sproxton)
(There is also a John HAND birth registered same district in Mar Qtr 1856 - and a death registered Dec Qtr 1856, which may be the same, can't find him on 1861 Census)
In 1861, a John H HAND age 4 is a visitor in Household of John and Sarah BARNES, in Branston, Leicestershire. Sarah is ages 50, b Sproxton. She may be a paternal Aunt?
FreeBMD has a marriage:
John BARNES
Sarah HAND
Dec Qtr 1840 Melton Mowbray
The IGI has the following:
BIRTH
John Henry HAND - 8 Jan 1856 Sproxton - Parents: John HAND and Mary
FreeBMD has a marriage:
Melton Mowbray - Mar Qtr 1845
John HAND and Mary WYER on the same page
Very possibly, as often happened, the death certificate is in error by naming his mother as Elizabeth. Does his NSW marriage certificate name his parents?
Do the Australian records give an occupation for his father?
Cheers
AMBLY