Rabbits are a serious mammalian pest and invasive species in Australia causing millions of dollars of damage to crops. Rabbits were introduced to Australia in the 18th century with the First Fleet and became widespread after an outbreak caused by an 1859 release.ince their introduction from Europe in the 19th century, the effect of rabbits on the ecology of Australia has been devastating. They are suspected of being the most significant known factor in species loss in Australia.