Bridget Noon born 1845, Nenagh. This would be a parish record.
Looking to Griffith Valuation 1850 which is used as a census
substitute for the times. There are no Noon's in either Tipperary North Riding or South Riding.
There are Neill's. Possibly Ann Neil went home for the delivery and that is why Bridget is baptised there.
The Parish of Nenagh is in Tipperary North Riding. There are no Neil's (spelling mostly Neal) there, although there are 20 Neil's in other parish's.
22 Neal(Neil spelling most used)
Nenagh is not only a townland but a Parish and a Union. A Union covers an area of a 12mi containing parish's, townlands and villages.
The Union's in Tipperary North are Roscrea, Thurles, Tipperary and Nenagh.
Patrick Neil, Parish of Ballynaclough, Townland Ballyvanran,
Poor Law Union Nenagh, tenant of Hon. O.F.G.Toler
#3 house land, outbuildings and land 28.1.24
Patrick Neil, Parish of Youghalarra, Townland Curraghtemple
Poor Law Union Nenagh, tenant of John Touhy
#3 land 17 acres 3 roods 5 perches
added to #2? (first time I've seen this and not sure what it means as #2 is John Touhy's land?
I have the civil registrations for Ireland on CD. 1864-1875. There is a Bridget Noon (no father listed-single mother) who had a son John 17 April, 1873 Roscrea, Tipperary.
Too late for your Bridget if she went to Australia in 1863
The Griffith Valuation has John Noon's listed 3 Galway, 1 Kildare, 4 Mayo & 3 Roscommon, 2 Sligo.
There is a John Noon, born Galway age 50 died in WWI Aug 26, 1914, Private in the Manchester Reg. 2nd. Battalion.
I found a Roscommon birth of Bridget by Joannis (John)
Noon 1 May 1845, wife Margarittae King, Killucan Ballinameena
Tipperary N. borders Offaly, Clare, Limerick, Laois and Galway.
There are 8 Noon or Noon's listed in the irish telephone book, when entering Tipperary there are a three in Dublin, others Cork, Kildare, Rathangan, Monsterevin. Over 100 Neil's but only a few in Nenagh.
Tipperary N & S Riding's both belong to an Irish History
Foundation that has the parish records you would be looking for. This is a not for profit but fee paying website - little free in Ireland. They should have Bridget's birth and you have her parents names which is a plus. The Parish of Nenagh has RC baptisms and marriages back to 1792 with gaps but baptiss continuous from 1845 and marriages from 1819. You will have to hope that the whole year 1845 is covered and that she wasn't born earlier. Ages are often widely off the mark.
I think that is your best bet at the moment.
No John Noon's in the 1901 census for Tipperary nor an Ann Noon but they would be in their 70's.