Kate Hill was receiving hormone treatment for polycystic ovary syndrome, a condition that meant she was not ovulating.
She apparently conceived twins at different times despite only having unprotected sex once during that time.
It is very rare for a woman to conceive a second time when already pregnant.
Most twins are the result of a woman releasing two eggs at the same time, or, less commonly, a fertilised egg subsequently splitting into two.
The twin girls, Charlotte and Olivia, were born 10 months ago with different sizes, weights and gestational development, according to reports.
“We actually did not realise how special that was until they were born,” Mrs Hill told Australia’s Seven Network.
Pregnancy normally stops the monthly cycle of ovulation but very rarely a woman can release another egg after conceiving. If this is fertilised it could also implant and develop into a healthy pregnancy.
It is believed only 10 cases of the phenomenon, known as superfoetation, have been documented across the world.
Speaking about the rare conception, Mrs Hill’s husband Peter joked: “Hole in one, maybe.”
The couple’s obstetrician Brad Armstrong said the condition was so rare he was forced to search for it online.
“I could not find any literature in the medical review websites at all,” he said.