Daughter of James Peek and his wife Deborah (née Pinder), Harriet was fourth of eight children. In 1849, when she was eight, she came to SA from Long Sutton, Lincolnshire with her family on the William Watson. Her mother died the following year. The family lived in North Adelaide and Harriet studied under Mrs Evans (Maude Jean Franc). In 1883 she married the thrice-widowed Frederick Henry Rix, who had worked for the Register, and opened the firm's branch at Port Adelaide. They lived at Hammond for 23 years and in 1906 returned to North Adelaide, where Mr Rix died four years later.
Harriet wrote for the press all her life, keeping a scrapbook of her articles and short stories. She also wrote a serial, "The House With Crooked Chimneys" based on early times in North Adelaide. In c.1921 she was awarded first-class honorary mention for an Australian story by the Ballarat (South Street) competitions.
In her later years, Harriet Rix lived at Prospect.