Hi Melanie and Elwyn, took an interest in this as I have a Farrell lady in my paternal line born circa 1820 in Longford. As Elwyn says the name is pretty much everywhere, I looked up the name in McLysaghts Surnames of Ireland and it states it is O Fearghail which from the Gaelic means "Man of Valour" the chief of the family back in history was from Longford, a county and town in the midlands of Ireland.
There are a number of Irish private Facebook pages doing genealogy and also all Ireland ones, most counties appear to have a few, a warning however a lot of people are in your position searching at the outer reaches of Irish records, 1800 plus or minus 20 years or so, also not sure of where exactly they are from, there are also a numberof them using Gedmatch programs based on local areas to see what they can find but in my experience while interesting it is difficult to find matches who are more aware than you will be. Any of them I am on are well moderated, helpful and polite.
Good Luck
Pat