This really needs some more work to verify. She appears in DPB (but not Burke's) as Joan Cecile b 1926 twin dau of Cecil George COTTER (1900-1948) descended from the 6th son of the 4th son of the 4th son of the
1st Baronet Cotter (I 1763), and unknown spouse/partner. She m (1) ? and (2) Vern [Vernon?] McCONNACHIE.
A search on Ancestry came up with a memorial record for "Joan Cecile McCONACHY" died 18 Aug 2001 (cremated 21 Aug 2001) aged 74 for Toowoomba Garden of Remembrance, Queensland, Australia. This could match a birth in 1926. I think it likely that DPB got the surname of her husband wrong but obviously more information is needed to substantiate the identification.