There is not much information on them in the indexes other than she was NOT deceased by 1901.
Harold Leslie SOUTTER was born to parents Edwin Walter Soutter & Rose Hannah BROWN in 1908 Brighton Victoria so that rules out her death in 1901.
there is no marriage record that I could locate for Rose Hannah & Edwin / Edmund / Walter (as he is listed in the indexes)
I note that Edmund Walter Soutter married in 1918 to Bertha Elizabeth Hornsby and had a fair few children and lived in Mildura.
You mentioned that Walter & Rose Hannah had 2 sons.. Harold can be located who was the other one ?
Rose Hannah's birth is not listed in either Victoria or Tasmania.
HOWEVER... I did locate a coroners Inquest for a Rose Anna BROWN 1973 "clothing caught fire"
Is there any further info you can provide so that I can look further ?
Do you have the marriage certificate of Walter & Bertha Hornsby ?