I think George is son of William JACKSON and Margaret BRAYSON, but you need to find baptism records......start with St Peters........to confirm this.
Information from the marriage certificate is really important. Catherine cannot read or write, so note her name at daughter's birth registration....and possibly any other occasion when Catherine gives her name.
Marriage https://familysearch.org/pal:/MM9.3.1/TH-1951-35348-14-57? 4 March 1873 St Peters Hamilton C of E George Thomas JACKSON 18yrs labourer bachelor Catherine SHAW 21yrs servant(her mark) Officiating Minister George WRIGHT witnesses Charles FROST, Selina FINDEN
birth Margaret Eliza JACKSON 25 Nov 1873 registered 11 Dec 1873 https://familysearch.org/pal:/MM9.3.1/TH-1942-35350-14503-12? Father George JACKSON, shoemaker, mother Catherine JACKSON formerly THAW, mother is informant.
Cornwall Chronicle 7 Oct 1865 http://trove.nla.gov.au/ndp/del/article/72359250http://trove.nla.gov.au/ndp/del/article/72359250? Death of Margaret JACKSON, living with Charles FROST at Hamilton, Constable FINDON investigating. From inquest file TAHO, Margaret is widow.
Marriage William JACKSON 50yrs Margaret BRAYSON 21yrs Hamilton 659 / 1843
children William James1844Hamilton Rachel Eliza1847 Hamilton Samuel1849 Hamilton male1852 Hamilton male1854 Hamilton
Your George might be male 1854. You need to look at baptisms St Peters Hamiltonfor these children, and names for two youngest children.
death William JACKSON 20 Jul 186076yrsHamilton Margaret JACKSON24 Sep 186546yrsHamilton
this Margaret could be the widow living with Charles FROST in Hamilton 1865.
See TAHO Permission to Marry file for William JACKSON and Margaret BRAYSON