Possibly Mollie's mother - especially taking into account Alice May's mother's surname and Mollie's second forename:
Tasmania
Alice May CRUSE
Birth Date: 23 Dec 1898
Registration Year: 1899
Registration Place: Lyell, Tasmania, Australia
Father: Albert E Cruse
Mother: Margaret Gwynne
Alice May BIRD is also buried at Devonport, died 5 April 1957, aged 59
Marriage of parents of Alice May CRUSE:
South Australia, 1896, p 680, vol 189, registered Adelaide
Albert Ernest CRUSE
Father's name: John Owen Cruse
Spouse Name: Margaret GWYNN
Spouse's Father's Name: Robert Gwynn
Marriage Date: 30 Nov 1896
Marriage Place: Res Of Albert Rowe Goodwood West
Possible birth for Ernest CRUSE (same person??)
Tasmania, 1864, registered at Longford, #1180
Erest (sic) CRUSE
Birth Date: 14 Nov 1864
Father: John Cruse
Mother: Martha Frampton
Marriage of Ernest CRUSE's parents.
Tasmania, registered Launceston, 1843, #614
John CRUSE, Martha Frampton (sic)
Marriage Date: 02 Oct 1843
John CRUSE died 21 June 1889, aged 78, buried Methodist section of Longford cemetery.
Martha CRUSE died 17 July, 1912, aged 87, buried Methodist section of Longford cemetery.
I see some immigration details for these people - happy to transcribe if you would like them.
You would need to get some certificates to validate these suggestions.
Judith