Kelly is such a common name in Ireland that it would be very difficult to research - you'd be knee deep in them!
Hartnett on the otherhand is less common and additionally, couples usually married in the Bride's parish - so it is worth checking that out carefully.
There were a lot of Hartnett families listed in Limerick at the time of Griffiths Valuation c. 1850. As only the Head of the Household was listed, I'd hope to find Catherine's Mother or Father listed. Do you happen to know their names?
As a huge percentage of these Hartnett families were in living in either Abbeyfeale or Killeedy parishes - I would check out any records for those area first, if only to eliminate them.
Did Catherine have any brothers that you know of? Could any of these have been named after her father?
Cheers