You have to consider the total lack of native predators in the equation. With nothing to really keep them in check the rabbits can breed and expand more readily. Plus, they have a fittness level different (mostly higher) than the similar niche organisms in Australia which gives them another edge.
Another example is the cane toad. When you think of "swarm"-type populations how readily are you to think toads?? But some parts of Australia are literally swarming with toads and the wave is expanding.