I had a Sheehy from "Abbeyfeale" in the NSW records. A dead end until I realised the parents were supposed to be from Listowel in the same NSW records. So I check the Parish in between Abbeyfeale & Listowell, and success (i was lucky I guessed the right Parish first off), and found the actual 1844 baptism (they migrated in the late 1840s ending up on the Monaro) it turns out the family was from Duagh Parish in Kerry. As this Parish is mentioned in your notes, I would start by combing the Duagh Parish records at registers.nli.ie, starting with the years you've got or guessed for baptisms. My Sheehys were from the townland of Scrahan in Duagh which is much closer to Abbeyfeale in County Limerick, than Listowell in County Kerry, despite Duagh being a Kerry Parish. By crossreferencing witht the Griffiths evaluations of the late 1830s I could work out the likely actual address (Scrahan being a particularly small townland)(but full of Sheehys).
Besides the townland the bpatism record will most likely list the Parents, and god parents, but it is not always clear. If you need help with a record or two, once you've found a likely drop a reply here and I'll see what I can do.
I have had great delight in telling the family they are all Kerrymen, by about 6km.