I'm sorry I got it wrong that Robert was born in Douglas. I've checked with what I have and nothing says Douglas, only Isle of Man.
All the information I have is 3 censuses:

1841 Census:
H0107/558/2 folio 9 page 9 Liverpool Lancashire
Finch? Place?

Robert Goldsmith age 30 Joiner J not born in county
Elizabeth age 30 not born in county
Elizabeth age 7 born in county
Mary age 2 born in county
Grace age 3 months born in county

1851 Census:
6, Court 5, Hotham Street, Liverpool
GOLDSMITH, Robert Head Married 1808 Journeyman Joiner Isle of Man
GOLDSMITH, Elizabeth 1809 Isle of Man
GOLDSMITH, Elizabeth Dau 1837 Liverpool
GOLDSMITH, Mary Ann Dau12 1839 Liverpool
GOLDSMITH, Grace Dau 10 1841 Liverpool
GOLDSMITH, William Son 8 1843 Liverpool

1861 Census:
RG9/2689 folio 111 page 28 Liverpool Lancashire

Elizabeth Goldsmith widow age 53 Douglas Isle of Man
Elizabeth dau age 27 servant Douglas