I assume you have seen the actual death notice in the Adelaide Advertiser (from beta newspaper site) Wed 14 December, 1904.
THALLON On 13 December, 1904 at Childers ST, North Adelaide, Catherine, the beloved wife of Henry Thallon, aged 68 years.
On page 2 of that issue of the paper is the funeral notice but it only mentions the husband and the address. Burial was at North Road cemetery.
So, if this age is correct, this gives a birth year of 1835/6 - could easily be incorrect, though.
Victorian birth certificates give good information so perhaps, at a pinch, there might just be a clue about her previous surname and children, from a birth certificate of one of her Victorian-born children. But then again.........
Judith