Is her second name Catherine and that is what she was known as? Her father's death notice does not mention Teresa, but does mention a Catherine, still living.
Sources
http:/warwicktaylor.com
NSW Gov, Birth Certificate - Teresa C. Frazier (10852/1872
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DNA Connections
It may be possible to confirm family relationships with Teresa 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 Teresa: