The death record in the NSW BMD (http://www.bdm.nsw.gov.au/
) gives us her father's forename so that we now know his name was John Walker...
25900/1967 NOBLET EDNA MAY JOHN ADA MURRAY ST LEONARDS
I'm not sure how complete the WA records are but they do at least contain Edna's parents marriage in 1905...
WALKER JOHN Male WHITFORD ADA MURRAY Female PERTH (reg num=) 1485 1905
Its not possible to tell from the information available which John Walker birth might be his (if indeed he was born in WA at all)...
WALKER JOHN JOHN STEVENSON JANE YORK 28313 1885
WALKER HENRY JOHN WILLIAM WILLIAMS MARY ANN ALBANY 16334 1875
Unfortunately, there are no Whitford births that I can see at all in this online facility.
Perhaps they were immigrants or moved interstate?