Hello Evelyn,

You may have seen that the IGI has Anne's surname at their marriage as FICK:

WILLIAM MOORE Marriages:
Spouse: ANNE FICK
Marriage: 15 JUN 1839 Patrick, Isle Of Man
Husband Age at Marriage: 20
Wife Age at Marriage: 20

If you are not a member I suggest you join the IOM FHS who will help you with information, especially while you are in the IOM, and will even open their library especially for you if your dates don't coincide with their opening times. They will also send you their mag which includes contact details.
Please see "How to join" at: www.iomfhs.im/

Because Moore was such a common surname in the IOM, with several families having the same forenames at the same time, it would also help you to find relatives if you could give more information. Did the whole family emigrate, or just John? Have you found them in censuses? Do you know anything further about John's parents?
Anne's surname (as Fick) is given in the Patrick bapts of Ellen 1839, Anne 1842, and Cath 1844, with Anne's and Catharine's entries also giving the town Dalby (Patrick), and in Mary Jane's 1864 bapt in German [IGI extracted entries, from the parish reg].
The other bapts don't have a surname for mother Anne, but Margaret 1847 and Catharine 1854 also have Dalby. There was also Sarah bapt Patrick in 1857 (no mother surname).
I couldn't find William Henry 1860, and although there was a Douglas 1853 bapt for John son of William Moore & Anne (no surname), I think John bapt 2 March 1851 Dalby, Isle Of Man looks more likely to be the same family as the other Dalby ones (but perhaps two Johns?) - where did you get his birth or bapt date from?

Sue