Daughter of the London-born Edward Walter Wickes and his wife Ann, Eliza married David Randall in 1840, when she was 19 and he 20. Her sister married David Randall's brother William. The Randall brothers and the Wickes decided to emigrate, first considering the south of France but rejecting this in favour of South Australia which they came to believe would have an equally beautiful climate with a better chance of profitable investment. Instrumental in this was George Fife Angas. While he was in the north of England giving lectures on the new colony of South Australia he went to David Randall's house in Northamptonshire in response to a letter of enquiry. He stayed a fortnight. David was enthused by the prospect of the colony and got together a party of forty emigrants, including shepherds and arrtisans, and their own family servants, and took them all out to South Australia at his own expense.
Eliza and her husband and two sons arrived in South Australia on the Templar in 1845. Her parents came on the same ship. Edward Wickes opened a school in North Adelaide, and later became secretary to the Board of Education. The Randalls lived in Adelaide for two years, in the house in Rundle St previously owned by William Giles, manager of the South Australia Company. They later lived in Upper Walkerville. They had nine children, including two sets of twins. They took up land at Dry Creek, but sold this and bought a dairy property at Mt Crawford. David Randall was nominated in 1851 for the district of Yatala, but turned it down because he spent so much time away from home on his properties. They went to live at Glen Para near Pewsey Vale. They also held land on the South Rhine in the Barossa, and near Gawler, and he was part-owner of the Mount Arden cattle run near Pt Augusta.
In about 1869, with David's health suffering, they sold Glen Para and moved to Seacombe House, at Brighton, 14 miles from Adelaide. On the death of Eliza's mother, they went to live at 'Lytton Lodge', North Adelaide, where her parents had lived, and where Eliza's father had opened a private school on his arrival in South Australia. David Randall died in England in 1874, and Eliza lived at 'Lytton Lodge' until her own death at the age of 83. Five of her children survived her.