In that case, I have found them

Looks like Thomas left earlier- see
www.ellisisland.org to view N.Y. passenger manifests.
23 Oct.1909 "Columbia" arrived New York from Londonderry, Ireland-
Jemima Moore (transcribed as Jamima), age 29, married
Children: Annie (9), William (7), Jacob (5), James (2 years 6 months), Thomas (11 months).
From Cullybackey; nearest relative in U.K. Jemima's sister Mrs. Eliza Wilson, Drumcon, Rasharkin; going to (husband/father) Thomas Moore, 19 Franklin Ave., Harrison, New Jersey.
They should now be found in 1910, 1920, 1930 and 1940 U.S. census records, etc.
Will ask the Canadian Moderator to move this thread to U.S. board so you won't have to start another one.