I wonder if this is the son William (tho' you had a middle name Frederick for him, where did that come from?) in 1861
RG9 603 54 18
High Street Shoreham
William H Harker? 26 Baker empl 1 man bn Brighton
Mary Ann wife 26 bn Hampshire
George Frederick son 4 mths bn Shoreham
Alfred James " nephew unm 19 journeyman baker bn Brighton
Elizabeth Cooper 8 neice bn Brighton
This is the first mention of a Cooper that we have found.
William's surname is indexed Harker, the image leaves me undecided - Harber could well be a possibility.
And we know he worked with his dad training as a Baker from 1851 census
so, back to my previous question - where have you seen him and Amelia as Harber-Cooper?