I think you are on the right track with Catherine being the daughter of John and Judy/Judith (not Johanna) - on your tree you have missed sibling Patrick who was born in 1847.
BAIRD - Friends of Mr. and Mrs PATRICK HART, Mr. THOMAS HART, and Mrs. MARGARET MILES and FAMILIES, and MR PETER CLARKE, are invited to attend the Funeral of their dear Sister, Sister-in-law, and Aunt to move from her late residence..........
http://trove.nla.gov.au/ndp/del/article/133901967Mother Judith might have remarried in 1854 to a Patrick GEARY?? You would need a transcription to find out, but we'll have a bit of a sticky around elsewhere first. She seems to have married John HART as a KELLY not O'NEIL - she is probably the Judith O'NEIL who married John KELLY - yay for you, she was a convict. No idea why there are two marriage entries showing, one in 1833 and one in 1837?????
Debra