Rodriguez was born Judith Catherine Green in Perth and grew up in Brisbane.
She was educated at Brisbane Girls Grammar School, and graduated from the University of Queensland with a Bachelor of Arts.
Following this she took up a tutorship at Kingston University, Jamaica, where she met her first husband, Colombian academic Fabio Rodriguez.
[1] She published numerous volumes of poetry, some illustrated by her own woodcuts, edited an anthology and the collected poems of Jennifer Rankin.
In 1989 she took up a lectureship in writing at Victoria College, which in 1993 became part of Deakin University, where she continued to teach until her retirement in 2003.