Diane, when searching the shipping lists, have a look for Patrick as well, especially if you don't find Fred! His age and bapt date were perfect for the birthday you gave, and I can't see Fred P. in IOM bapt records or in the 1841 census.
Patrick son of John Caley & Isabella Corkill bapt Maughold Parish Church on 26 Nov 1820.

Isabella Caley was in the 1841 Maughold census, at Ballakilley, aged 60, Ag lab, b. Isle of Man, with two of their children William (who was bapt Maughold 13 June 1818), a tailor, and Margaret aged 14 (bapt 29 Apr 1827). Patrick was working elsewhere in Maughold.

Isab CALEY aged 62 was buried Maughold Sept 8 1843. It looks as though John Caley was buried Maughold Jan 8 1832, although no age was given.
Patrick appears to have left the IOM between the 1841 and 1851 censuses.

If you find Fred P. in the passenger list hopefully he will be travelling with one of his siblings.

Sue