Elizabeth's birthday is listed as Mar 4 1867 on her birth certificate and it's listed as Mar 4 1864 on her death certificate, however her mother passed away in 1866. She was the daughter of William Peters and Jane Martell. Elizabeth passed away in 1955.
Sources
Birth registration and death certificate on NS Vital Records
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DNA Connections
It may be possible to confirm family relationships with Elizabeth by comparing test results with other carriers of her ancestors' mitochondrial DNA.
However, there are no known mtDNA test-takers in her direct maternal line.
It is likely that these autosomal DNA test-takers will share some percentage of DNA with Elizabeth:
https://www.novascotiagenealogy.com/ItemView.aspx?ImageFile=1955-2803&Event=death&ID=371982
https://www.novascotiagenealogy.com/ItemView.aspx?ImageFile=1803-9&Event=death&ID=4573, Jane (Martell) Peters died of consumption on April 3rd, 1866. Somehow, Elizabeth Maria Peters was then born to her 9 months later, per https://www.novascotiagenealogy.com/ItemView.aspx?ImageFile=1904-69500341&Event=birth&ID=252725, which is the source cited here.