Thanks Marie. After your previous message I was inspired to look in all the censuses for Robert & Catherine Moore - while I've got this 14 day free trial of Ancestry!

1881 Ballacottier, Onchan: Robert 55 farmer born Arbory, Caesar 15 b. Malew
1871 2 Oatland, St Anne: Robert 44 farmer b. Arbory, Caesar 4, b. Malew
1861 Ballafarrant, Malew: Robert 33 farmer born Malew
1851 Castletown Rd, Malew, Robert 25 Ag Lab born IOM
Ancestry.co doesn't do 1841, so your input there is particularly interesting, could take us back another generation.

I think the marriage to Catherine Sharp is probably correct given the 1891 census:

Ballahow, Santon
Robert Moore H m 65 Farmer b. Arbory
Catherine Moore w m 67 b. Rushen
James Moore son m 24 Farmer's son b. Malew
Caesar Moore son s 22 Farmer's son b. Malew
Mary A. Salthouse g.dau 13 Domestic servant b. Manchester
Ann Sharp aunt s 84 Living on own means b. Ireland
William Craine servt s 24 Farm servant b. Douglas
Joseph Ryan servt s 16 Farm servant b. Not Known

Although I don't think Ann Sharp could actually be Robert's own aunt.

Henry Moore: In the 1861 census when Robert & Catherine are at Ballafarrant, schedule 40 (f.76 p.10), at the next place, schedule 41, Ballafarrant, Flax Mill house, is
Henry Moore Head m 68 Fisherman b. Arbory
Eleanor Moore wife m 47 b. Malew
Margaret Creer stepdaughter 14 b. Malew

Robert & Catherine also have a son William Henry who is 4 on the 1861 census, born Malew.