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Brilliant, many thanks for your quick replies and explanations.  My approximations of letters weren't good enough to pull up the word!!  I am now assuming the babe did not survive either as I have found no further records. 
As another question (and maybe not the right forum) but is it possible the child would be buried with her?
Have a good day

Thanks, Judith, for your thoughts.

I am very happy to report that with the thoughts from RootsChat and Find a Grave, I have solved the mystery of Jane O'Brien.  She was born in 1862 and died in 1943 and is buried alongside her sisters, cousin (Charles Low) and George Smith at Woronora cemetery.  The confusing bit was she married George Frederick Smith who was initially the husband of her sister Eliza.  Eliza had died within months of her marriage to George. 
George died in 1947.

Many thanks again to you all.

I am curious about the obvious tick by the name Bridget Hoolagan who is 'mother of the groom'.
Through various documents her surname seems to be vary (woolahan/coolahan/callaghan) which make her very hard to trace. I assume this is due to pronunciation challenges, the spelling skills of the writer, interpreting the handwriting etc.

I have not been able to trace a death cert for Bridget and wondered if the tick indicates 'deceased'. Or perhaps the tick means her name has been checked as accurate at the time?!
I know John O'Brien and the Trumper parents are still alive at this time.
Any thoughts on the 'tick' would be appreciated!
Thanks in advance.

Thanks for your questioning.
A further obituary was placed in 'The Sydney Morning Herald Friday 23 Oct 1874':
"O'Brien - Oct 22 at her residence, Gloucester-terrace, Macquarie Street South, Jane, the beloved wife of John O'Brien coach trimmer, aged 38 years in childbed leaving an affectionate husband and seven children to mourn their loss".   
Although this doesn't identify the children by name, I have firmly identified 6 through a range of records, not so sure about young Jane (1862-) though.

Find a Grave has a photo of the headstone which records Jane (mother who died 1874), her mother also called Jane and her father called Charles Trumper, Emily Low, James and Emma Low (I think the Low family is part of the Trumper family), Alice O'Brien. John is also recorded here.  Unfortunately, the headstone is very hard to read in the photo. 
Rockwood General Cemetery:  Old Anglican Section A Plots 148-150 in S.A.G.

Frances, Annie Ada and Emily Harriet are buried at Woronora. Ellen is buried at Waverly Sect 6 Row 1.
Their sister Jane (1862-) is elusive in baptism, marriage and death!

Thanks again

Thank you Shanreagh for posing questions.

I am not sure if the information below will give a fresh eye to my question pertaining to who are Joseph O’ Brien and Bridget in Ireland and what became of Bridget.

Joseph (father) death cert records:
Date of death:  not recorded!
Age:  49 years
Buried: 30 May 1852
Abode: Infirmary. 
Quality or Profession:  Moffitt (ships name)  (The Moffitt is the boat that took them from Hobart to Sydney.  They originally arrived in Van Diemen’s Land on the Strathfieldsay in 1833.)
Ceremony performed:  Parish of St James, Cumberland Sydney.  Roman Catholic.

Children born to Joseph and Bridget O’Brien

1.    Cornelius   
Baptism:  1828 Dublin, Ireland
   Parents Recorded as: Joseph & Bridget O’Brien
Marriage:  1858 Sydney Australia, 
   Parents recorded as:  Joseph O’Brien and Bridget Coolaghan  (& both deceased)
   Spouse: Elisabeth Chislett
Died:  1865 Sydney. 
   Parents recorded as Joseph O’Brien (shoemaker)     Mother: unknown
   Informant:  wife

2.   Edward
Bapt:  1831 Dublin, Ireland
   Parents recorded as:  Joseph and Bridget O’Brien
Marriage:  1853 St Mary’s Cathedral Sydney Australia
   Parents:  there is no place on the official form for bride and groom to put parents names.
   Spouse:  Sarah Brennan
Died:  1877 Freemantle, Western Australia while visiting son .
   Parents recorded as:  Joseph O’Brien (bootmaker)  Mother : Unknown
   Informant:  Son.  Edward was visiting his son in Freemantle at the time of death.

3.   John
Bapt:  1834 Hobart, Tasmania or Van Diemans Land as it was known Roman Catholic   
   Parents recorded as:  Josephi O’Brien and Brigiae Houghlan
Marriage:  1858 Sydney. 
   Parents:   I am waiting for NSW BDM for the marriage info
   Spouse:  Jane Elizabeth Trumper
Death:  1917, Sydney
   Parents recorded as:  Joseph O’Brien and Bridget unknown
   Informant:  Son-in-law

4.   William
Bapt:  1837 Hobart at St Joseph’s Roman Catholic Church
   Parents recorded as:  Joseph and Bridget O’Brien
Marriage:  likely but unsure who to
Death:  1882 Sydney.  Due to a fall in a Sugar Factory. 
   Parents recorded as:  “Not stated O’Brien” and Mother “Not Stated”
   This record is very hard to read but it looks like the informant advised William’s brothers of his death and there also appears to be the word Widow along with this comment.  There was an inquest and articles in the Sydney newspapers but no mention of a wife or children.

5.   Joseph
Bapt: 11/03/1841 at St Mary’s Cathedral Sydney
   Parents:  Joseph O’Brien and Bridget Kologan.  Lived at Sussex Street
Death:  10months old 1841 at Sussex street, service at St Mary’s Cathedral
   Parents recorded as:  not named
   Obituary: none located

6.   Joseph (my Line)
Born:  01/09/1843.  Bapt: 01/10/1843 at St Mary’s Cathedral
   Parents recorded as :  Joseph O’Brien and Bridget Hallighan
Marriage:  1869 at 47 Barton Street Sydney.  (Previous research indicates no records will exist about this time of marriages at Barton Street).
   Parents recorded as:  space is blank
Death:  1901, Victoria (lived in Victoria for his last 13 years)
   Parents recorded as:  Joseph O’Brien-profession unknown,  Mother: Unknown
   Informant:  Local constabulary to JP

I have searched Trove and found that the children have submitted obituary notices in the papers for all their siblings (accepting the first wee Joseph who died aged 10 months).  Joseph’s wife placed an obituary in the Sydney newspapers even though they had been living in Victoria for 13 years.

 I have not found obituaries for their parents Joseph and Bridget.

Once again, thank you for reading my long post.  Any thoughts would be greatly appreciated.