Hi geveN,
Other methods of dingo control are baiting and shooting. The latest effort for many state governments was to reintroduce a bounty on dingos, that is, the government pays about AU$50 for each dingo killed. However, dingos resident in National Parks and reserves are protected. Wild dogs and dingos generally avoid humans, and aren't a problem in towns and cities (although foxes are).
The dingo is in a bad situation due to breeding with what are known as wild dogs. It is often difficult to distinguish between a wild dog and a dingo, but they are both considered pests by many farmers.
Pure bred dingos are becoming increasingly rare in the wild, though the species may be "safe" due to captive breeding. In fact a few people own pure bred dingos as pets, but I believe they are not ideal as the can be a bit agressive.
Dingos are mainly scavengers that feed on dead animals like kangaroos and rabbits, but they are known to prey upon lambs, and to a lesser extent young cattle. This is why the fence was built, to protect the sheep farms in the south east. But the dingo pays a high price for a few stock losses. The farm lobby in Australia is very powerful.
There is (fortunately) no rabies in Australia. The public is divided on how to deal with dingos. There was a famous murder trial in the 1980's where a women was falsely convicted for the murder of her baby, when 10 years later the babies clothes were found in a dingo cave in Ayers Rock. Another small child was killed by a dingo on Fraser Island about five years ago, so there is not a great deal of sympathy for the dingo's plight.
It's a bit like the Great White Shark debate here in Australia. Do we kill them becasue they pose a (small) risk to our lifestyle? Or do we protect them, and respect them for being an important part of the ecosystem? The debate goes on.