May I also offer some conjecture

22 June 1877 the ship ‘Commonwealth’ arrived in Sydney NSW. Onboard were many immigrants, including the following PICKERING family.
George, aged 33, a labourer, native place of Durham, Church of England, could read and write.
Alice, aged 29, also of Durham, CofE, and Read/Write
John G, aged 5, of Durham
Will Hy aged 1, of Durham, died during the voyage. (I think this wee lad was William Henry)
http://indexes.records.nsw.gov.au/ebook/list.aspx?Page=NRS5316/4_4800/Commonwealth_22%20Jun%201877/4_480000139.jpg&No=1 (scroll through to page 9 for the Pickering family listing and page 23 for the summary of the info).
George’s parents are named on some immigration documents held by NSW Archives and digitised by at least one commercial family history website. I read his parents as John & Eliz
h (of) Durham, and that he had a relative in the Colony, an Uncle, James CUMMINS, of Newcastle. The same document has Alice’s parents as B.D. … so un-named, and ‘both dead’.
RChat’s NSW resources board includes live links to the parish registers for the Christ Church Cathedral, Newcastle NSW.
https://www.rootschat.com/forum/australia-resources-offers/ then to the NSW resources, then to reply #3 and part of it includes the following:
Baptisms, Marriages, Burials, Christ Church Cathedral, Newcastle
http://www.flickr.com/photos/uon/sets/72157606066769147/ 1820 – 1899 Family Register
http://www.flickr.com/photos/uon/sets/72157605008173551/ 1826 – 1837 Baptisms, Marriages, Burials
http://www.flickr.com/photos/uon/sets/72157604433014652/ 1837 – 1838 Baptisms, Marriages, Burials
http://www.flickr.com/photos/uon/sets/72157605132739200/ 1839 – 1861 Baptisms, Marriages, Burials
http://www.flickr.com/photos/uon/sets/72157605674610949/ 1856 – 1868 Marriages Register
http://www.flickr.com/photos/uon/sets/72157605785759029/ 1869 – 1885 Marriages Register
http://www.flickr.com/photos/uon/sets/72157605802132868/ 1885 – 1897 Marriages Register
http://www.flickr.com/photos/uon/sets/72157606197590347/ 1899 – 1913 Marriages Register
http://www.flickr.com/photos/uon/sets/72157605928662968/ 1913 – 1914 Marriages Register
http://www.flickr.com/photos/uon/sets/72157606308436455/ 1914 – 1916 Marriages Register
http://www.flickr.com/photos/uon/sets/72157606323070651/ 1916 – 1918 Marriages Register
http://www.flickr.com/photos/uon/sets/72157606450662513/ 1918 – 1929 Marriage Register
http://www.flickr.com/photos/uon/sets/72157606952230042/ 1929 – 1936 Marriages Register
Hopefully that info will be helpful.
I should also carefully note that the Christ Church Cathedral is actually in the Newcastle suburb of Hexham, and Hexham in the county of Northumberland in NSW is so named in honour of Hexham, Northumberland, England.
JM