Alongside future Neighbours castmate Janet Andrewartha, Woodburne attended the National Theatre Drama School and graduated in 1980. Woodburne played Josie in the television miniseries Outbreak of Love. Woodburne starred in the ABC Film 1915 as Dianne, alongside Sigrid Thornton, Scott McGregor and Scott Burgess. Woodburne said the fighting is not the only focus of the miniseries, as it shows how the lives of the women were also affected by World War I. In 1990, she auditioned for the role of Pippa Fletcher in Home and Away, but lost out to Debra Lawrance.

In 2005, she was nominated for the Best Female Performance in a Soap Opera award at the international Rose d’Or television festival, but was beaten by fellow British actress Lesley-Anne Down.

In 2014 she became the lead in Night Terrace, a narrative comedy audio series in which she told TVTonight she plays “basically a female Doctor Who”. The series was produced by Splendid Chaps Productions, with the first season released at the end of 2014. It won the Convenors’ Award for Excellence in the 2014 Aurealis Awards. A second season was released in February 2016, also starring Woodburne. Both seasons have been licensed for broadcast, with the first commencing on BBC Radio 4 Extra on Sunday 21 April 2019 as part of The 7th Dimension programming block.

Woodburne appeared in a documentary special celebrating Neighbours’ 30th anniversary titled Neighbours 30th: The Stars Reunite, which aired in Australia and the UK in March 2015.