I am also researching a Timothy McCarthy who was born about 1824 in Cork. From comparing to other family trees, I believe he came from Knockagarry, married someone named Mary, and moved to America between 1830 and 1854. He is my great great great grandfather. I would love to exchange information with anyone who is researching the same line.
Timothy, who went by Tim later in life, told him son Michael, who told my great aunt Bonnie, that the family is descended from the king of Munster. I doubt it to be true, but it is worth repeating.
He settled in Indiana and Michael was born in 1865, so it is possible that a link is missing in the family history there (since Tim would have been 40), which would account for the number of chilren I have found references to (10). Michael later moved to Wyoming after having Blair Blodgett (my great grandfather) who instead moved to Virginia and had Thomas Blair (my grandfather) who lived in a dozen states throughout his life.