Hi Jennifer
This is indeed a tricky one. I've searched all over and can't find Birdoneau. The closest I have come to it is BRIDONEAU - There is a Catherine Bridoneau co author of a book selling on Amazon and a Jacques Bridoneau who died in a French Hospital on 9th July 1754 aged 16 "ans".
What I have found though is EMMA J. WHELAN who was born in Bega New South Wales in 1895. Her father was Thomas Whelan and her mother was Elizabeth (no surname given in the index). Birth reference no. is 20547/1895.
I had a look at the 1881 Canadian Census but there was no ELZERD LE PINE or any BIRDONEAU or BRIDONEAU families there.
I don't have access to the 1891 Canadian Census, but it might be worth having a look at if you haven't already done so. Best of luck with your research. Trish