Rabbits are not native to Australia.  The first Rabbits were brought out in 1788 with the first fleet of British settlers.  But it was not until 1859 when European Wild Rabbits, Oryctolagus cuniculus, were deliberately released for recreational hunting that they started to become a problem on the mainland of Australia.

Ecological Disaster

The combination of grazing animals like Sheep, Cattle, Goats, Camels, Horses, Donkeys and others with Rabbits and introduced of feral predators especially the Fox and the Cat destroyed the ecosystem that had been present before, replacing it with one totally out of balance,  This was made worse by the vast scale clearing of the Australian vegetation.

Spreading

The Rabbits in Australia spread over the continent probably faster than any other non flying animal has ever spread over a continent.

Unfair

It is unfair to blame the Rabbit.  They never asked to be brought to Australia.  They are also not the only thing that needs to be removed from the Australian countryside.

Inconsistent

If you had a pet Rabbit that you wanted to get rid of and deliberately infected it with a disease that you knew would condemn the animal to a slow and painful death you would probably be sent to prison for a long time.  Many people would approve of your punishment.

There is a saying that two wrongs do not make a right.  But an agency of the democratically elected Australian government of the time brought Myxomatosis to Australia and killed over a Billion Rabbits.  Do a billion wrongs make a right?

Myxomatosis did not even solve the problem; it just reduced the numbers of Rabbits.  The ones that were left were less suspensible to this terrible disease and built up in numbers.

When the numbers of Rabbits dropped suddenly, the Foxes eat other animals.  Not just the native herbivores, but also the native predators of the Rabbit.  Now there are fewer predators to eat the Rabbits.

Sometimes it seems that the laws against cruelty to animals are more related to aesthetics.  That is, if we can see the cruelty, it is illegal, but if it is not visible to us it is all right.

However, I have strayed into moral questions. 

Ecological Disaster

The introduction of Rabbits to Australia was an ecological disaster.  But we need to look critically at what other things we have done wrong and set out to reverse as much of the damage as possible.

The Rabbits in Australia need to be got rid of, but so do the Foxes, Feral Cats and Dogs as well as properly managing the grazing animals we use.

I do not advocate the mass killing of animals.  Drugs already exist that will make an animal permanently sterile.  They could be developed to be applicable on a continent wide application.  If all the feral animals in Australia were rendered sterile, they could live out their natural lives.

This is, perhaps, not a very practical solution, but something of the sort needs to be considered.

Failed

Our ancestors introduced a number of animals which are perfectly good in their own native lands, but totally unsuited to Australia.  The combination of these animals with direct Human interference in the landscape resulted in an ecology in much of Australia dominated by Rabbits, Foxes and Feral Cats.

Some of our attempts at fixing this problem have increased this domination. 

The Whole Ecosystem

Any further attempt to fix the problem needs to consider the whole ecosystem.  This especially applies to large scale projects like the importation of more exotic species.

Rabbits and Foxes

A successful predator of another species does not wipe out its prey species.  Foxes certainly eat Rabbits, both in their native ecosystem and in Australia.

However, although predator and prey which are adapted to each other form some sort of balance, this does not apply to ones not adapted to each other.

This situation happened in Australia when Foxes were released.  The native animals were not adapted to this new animal and many of then either became extinct or are now threatened with extinction.

The native predators that could potentially have controlled the Fox were either already extinct like the Thylacine, or greatly reduced in numbers like the Wedge-tailed Eagle.

When Rabbits were released the native predators were already in serious decline because of Human activities.  If Rabbits had been released without the other changes they would probably still have become a problem, but not a disaster.

Native Predators

It is frequently stated that Australia did not have native predators able to control rabbits.

This is absolute nonsense.

Native Rabbit Predators in Australia

Goannas

On Kangaroo Island where there are no Foxes, and less disturbance of the original ecosystem than on the mainland, Rabbits were introduced.  The Goannas found the Rabbits very tasty.  They would go down their burrows and eat the baby Rabbits.  Goannas will also eat adult Rabbits.  There are no Rabbits on Kangaroo Island now.

Wedge-tailed Eagles

The Wedge-tailed Eagle also likes the taste of Rabbits.  Rabbits make up a large part of their diet.  Contrary to earlier beliefs, they rarely kill lambs.  But these eagles were killed in the millions.  A bounty was put on them.  Incidentally they also eat Foxes.  I would guess that they might eat the odd feral Cat as well.

Quolls

Quolls are also Rabbit predators.

What if all the Foxes disappeared?

This is partially a thought experiment. 

If all the Foxes died overnight I would expect the initial effect to be an increase in Rabbit numbers.  The native predators would take sometime to build up on numbers to make a big difference in numbers of Rabbits.  But with the Foxes no longer around to eat the predators, they would build up.

But what if the Foxes were to be removed more slowly?

This is the case in Western Australia where large areas have been baited and the Fox numbers reduced.  The Sand Goanna which is a potentially major Rabbit predator is increasing in numbers. 

The main method of Fox baiting is with monofluoroacetate (1080) which is a poison naturally occurring in some Australian plants.  Native Australian animals tend to be quite resistant to it while introduced animals like the Fox are killed.

Daughterless Genes

It would be more humane if a gene could be introduced into the Fox population that meant that all the cubs born from a mating were male.

Sources

http://www.animalcontrol.com.au/rabbit.htm

http://www.easterbilby.com/eradication.html

http://www.wildaboutbritain.co.uk/forums/mammal-forums/6090-myxamatosis-rabbits.html