According to a message posted on this board by Brian Lawson on 4 February 2004, Elizabeth bp. 1826 and Robert bp. 1832 were children of Thomas Moore and Eleanor Kneen. Another contributor quotes the IGI with Rob. Moore marrying Jane Cowley at Braddan, 13/11/1858, with 4 children including Robert Stephen in 1866. Thus Robert S would be Elizabeth's nephew.
I have not checked for his baptism in the register myself yet, but I noticed
MNHL #106188 Braddan
1858 Nov 13 No.224
Rob. Moore, full age, Bach, Lab, Ballaquine, s. Thos Moore, Lab., &
Jane Cowley, full age, sp, - , Gt George St Douglas, d. Dan Cowley, farmer
His mark,

and also

1874 Nov 15 (no. 505) Kirk Braddan
Elizabeth Annie, d. of Thomas Cavendish & Jane Moore, Douglas, car proprietor
.