Hello Steve,
I first went looking for Elizabeth Mc Donnell and found her baptismal record on www.irishgenealogy.ie. She was baptised on 21st March 1875, born 16th March 1875 in Rthmines in Dublin. Father Patrick Mc Donnell, mother Elizabeth Byrne. This record is free to view on this website.
I then went looking for Elizabeth Byrne. I couldn't find her on this website (which deals with Co. Carlow) however I went to www.rootsireland.ie and found her there.
Baptism of Elizabeth Byrne, father Edward Byrne, mother Bridget McCabe, in 1849 in Co. Wicklow.
You would have to register with this site(free) but it will cost approx €5 to view and print this record.
It is possible that she was born in Co. Wicklow but grew up in Carlow?
I think it's important to realise that most people who emigrated were illiterate and undocumented. They didn't know how to spell their names and hadn't a clue as to what age they were. At the port of arrival their names were recorded phonetically, their ages were only guessed, and this is the information that followed them for the rest of their lives.
The proof of this occured in 1909 when the old age pension was introduced into ireland. People had to prove their ages and were forced to go through baptismal records to establish when they were born. That is why there is such HUGE discrepancies between ages in the 1901 census and the 1911 census of Ireland. Dates were found to be out by many many years in some cases.
Hope this all helps,
Kind regards,
Anne Dennehy