Rabbits were introduced to Australia in the 1800s and spread quickly across the continent, moving into the nests of native burrowing animals and eating their food. What allowed the nonnative rabbits to spread so quickly in Australia?

Unlike the native marsupials that have a very slow reproduction rate, the rabbits have a very quick one, so in a very short period of time they manage to outnumber the local population, and thus eat their food, and occupy their shelters.

- Lack of predators;

The predators in Australia are not a common site, and apart from the introduced species like the dingo, the fox, and the domestic cats that went feral, there aren't any others. On top of it, the populations of the dingo are very small and restricted to just few parts of Australia, while the foxes and the feral cats were still not in large enough numbers in the 1800's, so the rabbits thrived.