These are the Featherstones from the 1851 census index

FEATHERSTONE Francis 11 Douglas 2525 474 16
FEATHERSTONE Jane 6 Douglas 2525 474 16
FEATHERSTONE Mary 36 Douglas 2525 474 16
FEATHERSTONE Mary A. 3 mos Douglas 2525 474 16
FEATHERSTONE Patrick 38 Douglas 2525 474 16
FEATHERSTONE William 3 Douglas 2525 474 16

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The only Featherstone burial in Brian Lawson's burial index is this one which Frances mentioned:

FEATHERSTONE, Patrick 45 Braddan 10 Sep 1856

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There are no Featherstones on the island in 1861, so it looks as though the family left after Patrick's death, presumably with Catherine as a small child, plus any others who may have been born in the early-mid 1850s.

I've just found an interesting tree on Ancestry which has additional details eg how Patrick died. Unfortunately, the tree compiler hasn't got a Catherine Featherstone b 1855 listed amongst the children, but there is a suitable gap between Mary Ann in 1851 and James in 1857. It seems very unlikely that your Catherine Featherstone b 1855 IOM could belong to any other family.

Jean C