Hello Abby, I can find the birth of Elizabeth and a number of siblings all born over the next 15 years, I can find the siblings and Mary the mother in the 1901 census, no Peter or Elizabeth listed there and she has herself as the "head of family"
You have done a lot of the heavy lifting already so I am not sure if you are looking for family there or want to go back further, the name Hanlon is fairly common there as it was the name of the main family in the region when there were Chieftains etc
There was a very good site or is a very good site called Carlingford People but it went behind a paywall around the start of Covid, think it is about $20 dollars Canadian for a year, lots of old photos from the area, mainly the people, assuming it contains some from Omeath too.
There is also a private page for Louth Genealogy on Facebook if you are there and also a Louth DNA matching page on Gedmatch with a FB page which you also have to join. Remember here that the members are not necessirly from Louth.
This is the link to the Carlingford People site and I see it also lists graveyard inscriptions, you can read the names without joining and I see O'Hanlon and O'Hagan listed in areas you mention. https://www.carlingfordpeople.ie/ ;
As a matter of interest circa 1828 there was a lot of migration from the Omeath area to St John, New Brunswick, there is a long thread on this message board about it from a number of years back, a man in St John wrote a book about it, not now available except is some libraries.
This site here may interest you also, https://jbhall.clahs.ie/ and there is a Carlingford Louth & Cooley Peninsula private FB page mainly local photos of the area.
I live in Louth but the other end, 40 miles away so please feel free to follow up if I have missed the point of your query.
Good Luck
Pat
