Australian 'billycarts' were used as early as the 1880s. They were either literally drawn by a billygoat - hence the Australian name 'billycart'- or small two wheeled hand carts for which the name billycart had already become a generic term.
The term billycart is an Australian variation of the English goat cart which, like the dog cart, was originally an 18th and 19th century form of animal-propelled baby carriage. A later development - the mail cart - was a two wheeled vehicle based upon the postal delivery cart but designed to be pulled by children as a play thing. The British firm Simpson, Fawcett and Co advertised these in 1870 emphasising their exercise value. Harnessed goats were also used in a variation of this two wheeled cart - again using the term goat cart or 'go-cart'. These could still be seen providing rides on English beaches in the 1930s. The mail cart, which could hold a young child, was also a precursor to the modern pram (Jack Hampshire, 'Prams, Mail Carts and Bassinets', 1980, pp.24,34).
Anthony Hordern and Sons Ltd was advertising billycarts in Australia in the 1920s - these were essentially the two wheeled mailcarts of the late 19th century. However it was around this time or a little later that the 'modern' billycart developed as a fruit box with wheels or the more sophisticated H-shaped frame with rope controlled steering. These were probably home-made versions of commercially produced - and hence relatively expensive - pedal cars, trolley cars or flivvers (a 3 wheeled version of the hand-propelled trolley car). In the absence of pedals or hand cranks, these were pushed or ridden down hill.
In his 1952 memoir, Sydney bookseller James Tyrrell remembered as a boy using a 'billycart', or what was probably a form of mailcart cart/goat cart without the goat, to deliver books for Angus and Robertson (J.R Tyrrell, 'Old Books, old friends, old Sydney').