I couldn't find a birth/baptism record of Catherine Doran born Galway. There are 4 Catherine Dorans born in other counties around 1809 1808 Limerick 1809 Wicklow 1810 Armagh and 1810 Laois.
I did find 2 Thomas Fury born in Galway 1 in 1817 and 1 in 1819.
I couldn't find their marriage anywhere.
There is no public member tree on ancestry which has Catherine & Thomas.
Would it be possible that Catherine was born in a county other than Galway and / or not in 1809 (more like 1819 like Thomas)?
Can you tell me if they came to USA 7 where they settled.