She was possibly born on 17 May 1813, spent most of her adult life in London, and died sometime after 30 March 1869, when she was awarded £25 by the Royal Literary Fund.
The following biography is therefore tentative and incomplete, deduced from a comparison of published local and family histories, clues left by Eliza in her own writings, and a search of parish records and census data.
Her father was therefore almost certainly Alexander Home Stirling Rennie, born on 13 June 1797 in Kilsyth, Scotland, a physician who studied medicine at Marischal College, Aberdeen, and upon qualification moved to London between about 1818 and 1820.
Although it received mixed reviews, it was sufficiently promising to gain her access to literary salons and the companionship of leading figures of the day.
As a teenaged published author in London with a father who had already achieved some professional and social success, Rennie appears to have had many admirers and friends, including Mary Shelley and her literary set.
In Traits of Character, she describes a meeting with the Duke of Wellington, with whom she discussed her father and his support of William Wilberforce and the antislavery movement.
She produced a steady string of short stories for the periodicals of the day, and also writes about receiving a small legacy, possibly from her father's estate or from one of her wealthy admirers.
She also writes about her inordinate fondness for her pet terrier, which was dognapped on two occasions for ransom (apparently a popular crime in London in the mid-19th century).