Dear Denyse
I suppose there are at least two issues you could consider: (1) Kinvara RC records begin in 1831 so I would wonder if this is the correct place at all given that you have had no luck. When using RootsIreland did you confine the search only to Galway? I would widen it on the off-chance the family moved and Catherine was born elsewhere.
(2) This might be the parish. There are gaps in these records, meaning that some are missing for whatever reason and this obviously impacts on any search.
You may have to consider what other records you can use to fill this gap and it may well be a case of having to conduct an information gathering exercise so that when additional records become available then you will be in a position to consider what is relevant. It seems that from your lack of success that Catherine was born (potentially) prior to 1864 so there may not be a civil record of her birth. You may find that an actual visit to the place during your trip could yield the best results - even though there was a lot of emigration from that part of Ireland remaining families have a surprising ability to recall the names of older families in the area. I hope this helps.
Best wishes
Clare
Genealogy Support