Thank you for the information about those two newspaper items re. death 1893 James DOYLE.
I am using Ancestry to find electoral roll entries, but the franchise was extended to women later than 1900 so there would not be an entry for this Elizabeth DOYLE, and it does look promising -
4058/1900
Elizabeth A DOYLE, parents James, Sarah. WOLLAHRA
If you are a direct descendent of James DOYLE and Sarah ATWILL it would be through BECKHAUS family? What do you know about this family (who would have DOYLE cousins)....I can see them in later Liverpool registrations.
Or is this DOYLE / ATWILL family of secondary interest to you........sibling of your direct ancestor?
This usually determines how much money you want to spend on certificates.
The HULLICK marriage is a significant breakthrough, and gives you another name to work with.
I suspect that there is not much more to find for Sarah A b. 1868, and Elizabeth Hannah b. 1873. Having tried obvious marriages, and subsequent deaths for parents' names, this line of enquiry would seem to be exhausted, and obviously limited by transcription accuracy.
I think you need to buy a relevant BDM certificate. An enquiry to cemetery would also be useful as family members are often buried with or near each other. Newspaper death notices, where they exist, would give name of cemetery.
The marriage certificate for DOYLE Aris M m. HULLOCK Leslie T 1898 SYDNEY #2646
might have Elizabeth Hannah as witness.
The death certificate for 13222/1925 DOYLE James J P James / Sarah M LIVERPOOL
might have a sister as informant.
The death certificate for 4058/1900 Elizabeth A DOYLE, parents James, Sarah. WOLLAHRA
would identify her by parents' names.
It seems odd that Mary J DOYLE b. 1862 is only the second birth in ten years to this couple?
The birth certificate for Ann b. 1857 or Mary J b. 1862, would be interesting for details of previous issue.
No obvious death to see for Sarah M DOYLE b. 1868, but I wonder if the third daughter alive at 1893 is not Sarah, but another daughter born 1852 - 1862 with birth not recorded?.