RootsChat.Com

Margaret Agnes SMITH, daughter of Francis Harmon SMITH birth was registered in 1912 in Adelaide ( 891/330).
http://www.rootschat.com/links/01ssn/

So presumably Francis and Hilda were married before 1912.

... and mother Hilda May WELCH

Surname: SMITH
Given Names: Margaret Agnes
Date of Birth: 11-Aug-1912
Gender: F
Father: Francis Harmon SMITH
Mother: Hilda May WELCH
Birth Residence: Adelaide
District: Adelaide
Book/Page: 891/330

Of interest - There is a birth notice on 1 May 1920 for a child of H TAYLOR and Annie (nee NAISBIT) of the same address as above - 173 Sturt St.
https://trove.nla.gov.au/newspaper/article/37515343  (1st column, bottom)

Harold TAYLOR married Annie May NAISBIT in 1919 registered at Norwood (279/313). A possibility - there is a birth for a Harold TAYLOR son of Thomas TAYLOR in 1895 in Adelaide (570/320). A brother /half brother of Hilda May?   

His army record (attestation Dec 1914) has the same address as Francis Harmer SMITH - Frederick Place off Sturt St. Father is Thomas TAYLOR
https://recordsearch.naa.gov.au/SearchNRetrieve/Gallery151/dist/JGalleryViewer.aspx?B=1930201&S=1&N=90&R=0#/SearchNRetrieve/NAAMedia/ShowImage.aspx?B=1930201&T=P&S=1
(note on page 10 in red says mother is Margaret TAYLOR)

Birth registration for Harold TAYLOR born 1895:
urname: TAYLOR
Given Names: Harold
Date of Birth: 30-Aug-1895
Gender: M
Father: Thomas TAYLOR
Mother: Maggie STOKES
Birth Residence: Adelaide
District: Adelaide
Book/Page: 570/320

Marriage registered for Thomas TAYLOR and Maggie STOKES :
Groom Surname: TAYLOR
Groom Given Names: Thomas
Bride Surname: STOKES
Bride Given Names: Maggie
Marriage Date: 25-Jun-1889
Marriage Place: Res of Rev E G Day Adelaide
Groom Age: 28
Groom Marital Status: S
Groom Father: George TAYLOR
Bride Age: 24
Bride Marital Status: S
Bride Father: Patrick STOKES
District: Adelaide
Book/Page: 159/854

Given that all of Hilda May's BDM registrations found in GenealogySA show her maiden name as WELCH, it looks as if she was conceived out of wedlock.

I am under the impression that births could not be registered for stillborn babies in South Australia in the 19th century.
I've never researched that but here is a link that seems to confirm it (search on "still" within the page) https://www.archives.sa.gov.au/finding-information/discover-our-collection/registration-of-life-events/registration-of-life-events
Added later: OTOH I have seen birth and death registrations for infants who lived only an hour.

Thanks. It's probably too much to hope they intend to fix some of the more annoying things they stuffed up in the "upgrade" a few years ago.
One of them being the excessive white space in the new layout for of the search page, which means that on my laptop I have to scroll far too often. Another being that when a search finds no matches it drops some of the search criteria. The blasted thing has NO IDEA which search criteria are most important to me and I frequently have to re-enter them.
Then there's that unbelievably patronising message and utterly irrelevant photo it shows when there are no search results. Admittedly no material harm, only to my patience. Also the colour scheme that actually includes PURPLE text for goodness sake.
Most annoying of all is that although they consulted left, right, and centre with every man company or government department his dog that wanted to get in on a success story but they didn't give the actual users an opportunity for input.  They didn't improve the search capabilities. Which already were fantastic of course but even something that fabulous can be improved upon (and not by just changing the way it looks!) For example - I'd love to be able to do a case sensitive search. Thinking of surnames such as Beer and Shell where it returns too many results.
I'll bet that upgrade cost tens of millions of dollars. A case sensitive search could possibly cost about a thousand, depending on what technology they are using.
Trove is fabulous of course and I am deeply grateful for it but the current management leaves a lot to be desired IMHO.

Yes, contacting cemetery management via the Enquiry form on their website is the way to go. Before management has a grave site destroyed they take a photo of the headstone(s), if any.
Yes, Cheltenham Cemetery used to be referred to as "the Woodville Cemetery" and the funeral notice means the burial was in the Catholic section.