Dawn,
Unfortunately in the 1800s Irish marriage certificates did not record mothers names, so tracing Elizabeth’s mother may involve some digging. Here’s a link to a copy of her marriage certificate. From it you will see that she was living in Kilmakee and that her father Joseph was a gardener. A John Fitzsimmons was a witness. Presumably a close relation.
https://civilrecords.irishgenealogy.ie/churchrecords/images/marriage_returns/marriages_1850/09391/5401827.pdf
Elizabeth was a minor when she married, so under 21. Tradition was to marry in the bride’s church which was Derriaghy Church of Ireland. So possibly she was baptised there. That church’s records go back to the 1600s. They are not on-line anywhere so far as I am aware but there is a copy in PRONI in Belfast.
The Valuation revision records list 2 Fitzsimmons houses in Kilmakee in 1862-1865. One (plot 1f) was occupied by a John Fitzsimmons and plot 1h by Margaret. Both were houses with small gardens. Margaret might be a widow, so might be Joseph’s wife. Her name remains as tenant till 1887. I can’t see a death after that that fits, so possibly he rname wasn't deleted when she died or left. Nor can I see a death for Joseph, suggesting he died pre 1864, which is when death registration began.
I did spot this Margaret Fitzsimmons who died in 1871, aged 67. She was a gardener’s widow and lived in Killeaton (which adjoins Kilmakee - so just a few hundred yards away):
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1871/020788/7292115.pdf
Can’t say it’s Joseph’s wife with any certainty but it might be. You would need to search the church records in PRONI. Those same records might also have his burial.
