Hello Sheila,
The Latter Day Saints (Mormon) records found on the Accony School website at acconyschool.com have records for Kilgeever Parish (Louisburgh, et. al.) that include the baptism records for four (4) children of John Jennings and Mary Gavin that appear to match your records. (Please note that the following dates are for "date of baptism," not "date of birth," although baptisms usually occurred soon after birth due to lower than average infant survival rates and the importance of Roman Catholic baptismal beliefs.)
Bridget Jennings is listed at the daughter of John Jennings and Mary Gavan, and Bridget was baptized on 13 December 1865, with M. Curley, PP, officiating and Anthony Malley and Cecily Lyons as sponsors.
Catherine Jennings is listed as the daughter of John Jennings and Mary Gavin, and Catherine was baptized on 25 March 1865, with P. Ryan, CC, officiating and Patrick Fergus and Honor Kelly as sponsors.
Honor Jennings is listed as the daughter of John Jennings and Mary Gavin, and Honor was baptized on 31 January 1860, with M. Hennelly, CC, officiating and Anthony Malley and Honor Davitt as sponsors.
Thaddeus Jennings is listed as the son of John Jennings and Mary Gavin, and Thaddeus was baptized on 12 August 1860, with M. Hennelly, CC, officiating and Thomas Jennings and Catherine Lyons as sponsors.
There are forty (40) "Jennings" listed as baptized children in these records with seven (7) listed with a "John Jennings" as the father, but only the above four (4) children have "John Jennings" as the father and "Mary Gavan/Gavin" as the mother. So, there could be 36 links to Jennings cousins to also consider (that is, the 40 "Jennings" baptisms minus the four (4) Jennings listed above). Analyzing all the Jennings and Gavin/Gavan listings might also provide you with more potential connections to our usual "needle in a haystack" searches.
Regarding the issue of children appearing in Ireland records, but not appearing in subsequent US records please consider, besides some very serious early death rates, that some of the older children may have been left behind with relatives for lack of funds for their passage to more distant immigration locations. The "fostering" of children with other relatives was fairly common in Ireland during those hard times when parents died or were otherwise unable to maintain the family. ("No money" for everyone's passage to America resulted in my great uncle---the oldest child in the family---being left behind in Ireland with his maternal grandparents.)
By the way, another interesting book that looks at "the hard times" of this period is "Paddy's Lament, Ireland 1846-1847, Prelude to Hatred" which gives a very intense look at the personal lives of the people living through those hard times, rather than a list of government statistics and issues.
Good luck with your research.