Hello Richard,
I am not related.
Before your great great grandmother Juila Mahony was born in 1827, and even before her older sister Ellen was born in 1825, her parents, Paul Mahony and Ellen Nagle had another child named Julia. This Julia would have died young, however.
A baptism transcription from the Find May Past (FMP) website shows the first-born Julia was baptized in the Mallow Catholic Parish on 15 July 1824. The transcription does not provide a first name for Julia's mother, but shows that her maiden name was Nagle. At the time of the baptism the family were living in Main Street. You can access the transcription after establishing a free account with FMP at: https://www.findmypast.com/transcript?id=IRE%2FPRS%2FBAP%2F1554412
Attached to the transcription is a link that takes you to a copy of the original Mallow Catholic Parish church register where Julia's birth was recorded. I accessed the link to the Mallow parish register. Julia's baptism is indicated by the blue arrow, as you can see here: https://i2.paste.pics/OI1LI.png
Julia's godfather is Tom Gavin. The name of Julia's godmother looks like M. Bennet.
You'll see initials in the right margin of the register that are in shadow, and extend into the spine of the register. The initials are hard to make out, but refer to the priest who baptized Julia on 15 June 1824. By coincidence, Julia was baptized 199 years ago today.
I also found that the Ellen Mahony who was born in 1825 had died young, as Paul Mahony and Ellen Nagle had another daughter named Ellen, who was baptized in Mallow on 19 June 1833. At the time of the baptism the family were living in New Street, Mallow. See the FMP transcription:
https://www.findmypast.com/transcript?id=IRE%2FPRS%2FBAP%2F1555844
A copy of the original baptism record shows that Ellen's godparents were Cornelius Connelly and Julia Carroll. Ellen was baptized by the Rev. D.M. Collins: https://i2.paste.pics/OI2R6.png
An Ordnance Survey Map of Mallow from the 1829 to 1841 time period shows the location of both Main Street and New Street. The map was accessed for free at the GeoHive website: https://i2.paste.pics/OI2TT.png
The map of Mallow shows that southwest of Main Street are the Brickfield; the Diocesan School; the Barracks; the R.C. Chapel where the Mahony children were likely baptized; the Canon Field; and the Church, which would be the Church of Ireland.
Northwest of Main Street is the Short Castle. Heading east from the Short Castle are the Brewery; the Parochial School; and the Depot. Crossing Fair Lane, still heading toward the east are the Bridewell (Jail); the Court House; the Market Place; and the Fair Green. The access road to the Market Place and the Fair Green is New Street, where the Mahony family were living when Ellen was baptized in 1833. New Street T-junctions into Main Street heading toward the southwest. Your Mallow ancestors would have been familiar with all these landmarks, having lived in Main Street and New Street.
I next looked for the church marriage record for Paul Mahony and Ellen Nagle in the Mallow Catholic Parish but didn't find it. I expanded the search for the marriage to all of County Cork, but again without results.
I also looked for Paul and Ellen's baptism records in Mallow but didn't find them either. According to the National Library of Ireland, Mallow baptisms go back to 1 January 1809, and are available to access until 5 February 1881, though there are gaps in the baptism registers. Paul and Ellen would have been born and baptized before 1809.
Marriages begin on 17 April 1757, and are available until 25 June 1881. There are also gaps in the Mallow marriage registers. See the National Library of Ireland website link: https://registers.nli.ie/parishes/0078
The old Catholic Church in Mallow is called St. Mary’s, and according to the mallowparish.ie website, the church was built in 1818, just six years before the first-born Julia Mahony was baptized in 1824: https://mallowparish.ie/ourchurches/
A Google Map of Mallow shows the location of Saint Mary’s Catholic Church, Main Street, and Market Square in William O’Brien Street. William O’Brien Street appears to be the present-day name of the former New Street. The map also shows the location of a business called “Nagle Fireplaces,” in Fair Street: https://tinyurl.com/2jhpy8ju
Bing Maps calls Main Street in Mallow, Thomas Davis Street: https://tinyurl.com/57e5nzrp
I didn’t have enough information to find information about your great great grandmother Julia, other than her baptism record, which I believe you already have.
Kind Regards,
Dave Boylan
SOURCES
Find My Past
National Library of Ireland
GeoHive: Ordnance Survey Maps
https://mallowparish.ie/ourchurches/
Google Maps
Bing Maps