Hi there,
http://investigator.records.nsw.gov.au/ If you use the simple search option, two key words, (her surname followed by the word 'death') you should be able to determine if there was any need for her estate to be Probated. Not all estates need/ed to be submitted for Probate. It depends/ed on the estimated/known valuation of the estate, and the co-operation of the known next of kin (if no will) or the executor/rix named in the will and not on the existence of a will or the lack of a will. In NSW where there is/was no will found, then the Public Trustee could/can become involved.
http://investigator.records.nsw.gov.au/Entity.aspx?Path=%5CAgency%5C28 Also, as you have found the funeral notice, then perhaps you may be able to contact that firm (or its successor firm) still. Many of the funeral director firms that were established in the late 19thC are still operating today. Their archival material is often found to be extant. I presume that as you have her d.c. that the funeral details noted on that match up with the notice you found at Trove.
ADDINGAnother couple of thoughts
from her d.c.
there is information about the informant, perhaps if you seek some family history info about that person you may find further infomation about your person after her estrangement from her family.
there is information about her then usual residence, and historic electoral rolls are available for that era, including online at a commerical website and of course physicially at the NSW State Library in Macquarie St Sydney, and at other libraries.
Cheers, JM