The artist 'representing the first generation of colonial New Zealand artists who were to succeed as professional painters' was born at Diamond Harbour, Canterbury, New Zealand. On her family's second trip back to her father's native Scotland, she was enrolled at the Merchant Maiden School, Edinburgh, where she took art lessons (1876-9).

Returning home, she began as a foundation student at the Canterbury School of Art (CSA) in 1882. Starting as a flower painter, as many women training in art did, she became fascinated with native plants, providing her with opportunities to travel widely in 1886 and in 1891 (Chatham Islands). From 1883, she exhibited with the CSA and other New Zealand societies, winning a prize for a study of ferns in 1885. Having met the Australian flower painter, Ellis Rowan, she visited Melbourne, Australia in 1894 to hold a solo show, which was met with glowing reviews.

In 1899 she travelled back to Europe, initially studying with Louis GRIER at St Ives, where she was greatly influenced by the Newlyn school manner of working. That same year she travelled to Europe, possibly in the first instance with Norman GARSTIN. Later, in Paris, she studied under the expatriate American artist, Charles Augustus C Lasar (1856-1936) where he held his own atelier. After settling back in St Ives, she was visited by New Zealand friends Frances HODGKINS and Dorothy RICHMOND in 1902, and further extended her interest in landscape painting. Stoddart finally returned to New Zealand in 1907 and taught at the Canterbury School of Art, remaining a leading member of the arts community until her death in North Canterbury. A collection of her watercolour studies of native NZ flowers is in the Canterbury Museum, and she is represented in most major galleries there, with a large collection in McDougall. One of her titles, Old Cornish Orchard (c1902) was purchased in 2000 by the Christchurch Art Gallery Te Puna o Waiwhetu. A major retrospective, with accompanying book by Julie King, Flowers into Landscape (Christchurch: Robert McDougall Art Gallery), was held in 1997-8.