The tithe applotment records from Doonaha West in 1827 list a Daniel McCarty with 9 acres of land, so you know the family were farming there then. Griffiths Valuation in 1855 lists Daniel McCarthy on plot 20a in the townland, which was a farm of just over 16 acres. (These two Daniels might not necessarily be the same person. They could be father and son etc). There are no McCarthy households in the townland by the time of the 1901 census.
The Valuation revision records in the Valuation Office in Dublin should tell you when he vacated that farm. Son Daniel was born in Doonaha West in July 1865 so the family were still there then.
I looked at statutory deaths 1865 – 1900 and see 4 possibles for Daniel, registered in Kilrush. 1880 aged 73, 1875 aged 45, 1878 aged 50, & 1869 aged 52. There’s about 27 Mary McCarthy deaths in the same period. Too many to make finding the right one easy.
I looked for a will for Daniel but he didn’t leave one, or at least not one that required probate.