Her death notice, from NLA Trove, gives children's names (see WA bdm online):
The West Australian, Monday 7 September 1953
CONWAY: On Sept. 4, 1953, Ellen, dearly loved wife of Patrick Conway, and loving mother of John (Canberra), Daniel, Gordon and Edward, fond mother-in-law of Joan and loved grandmother of Patrick and Terence. Privately interred in the Roman Catholic Cemetery, Karrakatta, Sept. 5, after Requiem Mass in the Star of the Sea Church, Cottesloe. Bowra and O'Dea, Funeral Directors, Perth. Requiescat in pace.
Looks like they stayed in Kalgoorlie-Boulder for a while after they married (where the 2 eldest chn were born).
CONWAY JOHN CORNELIUS : Service Number - 415511 : Date of birth - 26 Oct 1918 : Place of birth - BOULDER CITY WA : Place of enlistment - PERTH WA : Next of Kin - CONWAY PATRICK
CONWAY DANIEL THOMAS : Service Number - 415402 : Date of birth - 27 Sep 1920 : Place of birth - BOULDER WA : Place of enlistment - PERTH WA : Next of Kin - CONWAY PATRICK
Then Gordon C born in Fremantle in 1927, and Edward J in Fremantle in 1929 (likely death in 2002 on MCB WA site as Edward Jas, aged 73). Daniel died in 1996 aged 75.
Note Ellen's husband is the Patrick Joseph who died in 1971 in Nedlands (not the Fremantle one).
Marriages for the older two lads on Reverse Marriages WA site.