Hi Jean,
Just a few thoughts to help with your search. You make no mention of religion when referring to your "Fawcett" search, but for Irish records some indication as to whether the family was Roman Catholic or Protestant is absolutely vital. ? what religion was your known relatives?
If one searches the 1901 Census for Ireland one comes up with 300 odd individuals with the surname "Fawcett" almost all of some Protestant denomination. and although none are listed as living in Co. Wicklow surely some of them have to be descendants of your common ancestor.
When one searches the Civil Registers Birth , Marriages and Deaths for Ireland, one comes across only a few references for "Fawcett" in Co. Wicklow. There appears to be one family , a William Fawcett who Died in Rathdrum District Co. Wicklow in 1865 aged 85, and his Wife Grace Fawcett, died 1873 aged 84. Any way your relative could be connected to them ?
I also looked today at at reference books of Gravestone inscriptions for County Wicklow and the only ones for the whole period up to 1880 for any name even resembling "Fawcett" where those 2.
As you can see what I am doing is trying to find the area to look in, then and only then can one start to investigate church records for possible baptisms etc.
PS I came across a reference to a "Henry Fawcett" from Rathdrum, co Wicklow who died in Victoria in 1884. Does that connect to anyone of yours?
Cheers
Kevin (meath999) , my daughter lives in Co Wicklow hence the interest.