She was born in Adelaide, South Australia, on 21 August 1958, but now lives in Sydney, New South Wales. She attended All Hallows' School in Brisbane, Queensland. She was married to actor George Spartels from 1984 to 2006 and has two daughters.

Her acting career began early with a part in the series Bellbird in 1967. However, it was straight from graduating at National Institute of Dramatic Arts (NIDA) that she got her big break with the part of Esther Wolcott in the ABC series Seven Little Australians. Allegedly the producers had all but given up on the show, because they did not feel that they had found a suitable actress for the part, until they discovered Elizabeth. She was actually younger than actress Barbara Llewellyn, who played her stepdaughter Meg in the series, but producers felt that they both respectively suited and were convincing in their roles.

The ten-part series delivered huge ratings when it was broadcast in 1973, and was also the first ABC series to enjoy international acclaim. It went on to win three AFI (Australian Film Institute) awards and four Penguins, including best drama series and a Logies Award for Best New Talent for Elizabeth Alexander as the sweet-tempered Esther. The series is now available on DVD.