In 1861, there's a Goldsmith family living in Braddan:

Daniel 42 blacksmith b Bride
Ann 32 b Liverpool
Eliz Ann 15 b LP
Sarah Jane 13 b LP
Nathaniel 8 b LP
OLIVER 6 b LP
Thornley 3 b Ramsey
Percy under 1 b Braddan

Ann was alias Mathews.

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This is almost certainly the correct baptism for father of the family above, Daniel:

DANL GOLDSMITH Pedigree
Male

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Event(s):
Birth:
Christening: 22 SEP 1818 Bride, Isle Of Man, England

Death:
Burial:

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Parents:
Father: ROBERT GOLDSMITH Family
Mother: ANN YOUNG

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Messages:
Extracted birth or christening record for the locality listed in the record.

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Something which might link your Robert to this family of Robert Goldsmith and Ann Young is the use of the unusual christian name of Oliver.

The following baptism entry may be for a son of your Robert Goldsmith and Elizabeth Kneale, born not long after they'd moved over to Liverpool:

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OLIVER GOLDSMITH Pedigree
Male

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Event(s):
Birth:
Christening: 13 AUG 1837 Saint Peter, Liverpool, Lancashire, England

Death:
Burial:

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Parents:
Father: ROBERT GOLDSMITH Family
Mother: ELIZABETH

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Messages:
Extracted birth or christening record for locality listed in the record

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and his death age 3 ?

England & Wales, FreeBMD Death Index: 1837-1915
about Oliver Goldsmith
Name: Oliver Goldsmith
Date of Registration: Jul-Aug-Sep 1840
Registration district: Liverpool
Registration County: Lancashire
Volume: 20
Page: 326

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It's a bit tenuous, but it might be a little clue in linking your Robert b 1806 to Robert Goldsmith and Ann Young. And that inconvenient 23 Sept 1818 baptism for Robert son of RG and Ann Young could have been a rebaptism of a 12 yr old. It occurred the day after the baptism of Daniel (22 Sept 1818)

I'm suggesting that Oliver may have been a name from a previous generation of this family.

Jean C