There's a chance that a baptism record or a marriage record for Catherine could have her father's name on, although like the birth record, they typically didn't name the father of someone born out of wedlock and even when written his name is sometimes crossed out. The witnesses on her marriage record might be relatives, but there's no guarantee.
I'd definitely try looking for a death record for Mary Ann Kelly if it was my ancestor, but it might be a needle in a haystack job, especially since she could have married before she died, and if she left the baby with someone else and got work to support them she could have died in another parish.
There's a reasonable chance Catherine could be mentioned in the Workhouse records for the area, if she wasn't being brought up by relatives. The workhouse authorities may have been paying for her board.