This doesn't answer your question but may be helpful to build on:
In 1909 Ellen is enrolled to vote and has no second forename listed.
1914 at Bailey St, Clunes
Ellen COCHRANE, school teacher
1919 at 18 Lyons St south, Ballarat
Ellen COCHRANE, S S teacher (S S probably = State School)
1931 at 7 Park St, Ivanhoe
Ellen COCHRANE, school teacher
1942 at 409 Burwood Rd, Hawthorn
Ellen COCHRANE, home duties
1949 at 44 Mathoura Rd, South Yarra
Ellen COCHRANE, home duties
1958 at 37 Illawarra St, Williamstown
Ellen COCHRANE, home duties
1963 at 26 Dudley St, Eltham
Ellen COCHRANE, nil occupation
1963, 1968, 1972 at 8 a'Beckett St, Kew
Ellen COCHRANE, home duties
I do not see her after that - my access goes to 1980. There are no others of the same surname at any of her addresses after 1909. The other women listed all have a second forename.
Given that she seems to be a spinster, living in Kew, with no further electoral roll entries after 1972 perhaps this is her death
Victoria, 1973, # 19782
DEATH PLACE: Kew, Victoria
Ellen COCHRANE, 99
Father: David; Mother: Ann Carmichael
Please Note - this would need to be verified, speculation only!
Judith