I agree with Sue, Job Carpenter's death certificate is likely to have the family history information as per his wife, Sarah. As the index for Mary's birth in 1889 has Job and Sarah for her birth, and as Sarah was alive when Job died late December 1926, it is likely Sarah would be the informant on Job's death.
NSW BDM website here :
https://www.bdm.nsw.gov.au/Pages/family-history-research/registry-records.aspxshows us that since 1856, that death certificates (and thus official transcriptions of those d.c.) should include:
the deceased's
Full name, sex, age, date & place of death, place of residence, occupation and marital status.
Place of marriage, age when married, full name of spouse. Children's name and ages. Parents' names and mother's maiden name.
Cause of death and duration of last illness. Burial or cremation date and place. I agree with Dundee, it is rare that the married surname of the adult child of the deceased is recorded but the (Christian) names of the living and their then ages are given in chronological order,
If I had enough spare pennies to order two official transcriptions during the special offer period, for second choice and taking on board Sue's thoughts re a child providing the rego info, I would give serious consideration to ordering Dolly CARPENTER's birth cert... she married and became Mrs ONSLOW and ***
is mentioned in Job's obit. Dolly's birth is after May's 1894 death... so we should learn several critical aspects from Dolly's b.c.
So,
My first preference :
Job CARPENTER NSW BDM death cert reference #2542/1927
My second preference, if enough pennies available :
Dolly CARPENTER, NSW BDM birth cert reference # 31189/1899
JM *** My grey cells are falling over today, I cannot verify my own statement re where I learnt that Mrs F ONSLOW was Job's daughter... I will re-enrol in family history 101 at this rate