He is with his wife and children in 1861 but then Sophia is a widow in 1871 and by 1876 she is in NZ and marrying Thomas Blowers.
RG10/5758/135/11
Sophia Walter 42
Laura S Walter 10
Emma S Walter 8
Alfred Walter 6
Ellen E Walter 4
Roslin M Churchhill 34 visitor/servant
You need the marriage certificate for John and Sophia to get his father's name and occupation.
This site
http://www.jerseyheritage.org/research-centre says "For certificates pertaining to life events (Birth/Baptism, Marriage, Death/Burial) prior to 1842 we can make copies of transcriptions taken from original registers. For certificates of life events taking place after 1842 you will need to contact the Superintendent Registrar’s Office. You can view certificates or obtain copies from their office in the Royal Square. The Archive holds indexes to the post 1842 certificates in the help desk area should you wish to discover the relevant volume and page number before you visit the Registrar’s Office.