Improving the Situation

 http://www.dec.wa.gov.au/pdf/science/bio_audit/great_victoria_desert01_p343-350.pdf

To maintain the relatively good conservation status of the Great Victoria Desert, the Australian government and the native people need to maintain the conservation of the desert lands.  If possible, the government should declare even more of the desert as conservation regions, which would limit the possibility of agriculture and pastoral development should such a situation arise.  At the very least, leaving the desert alone should be sufficient since its harsh climate can protect itself fairly well. 

To handle the invasive animals, there first must be some effort to research their patterns as they move across the desert.  With more information, it can be possible to pinpoint the areas where these animals are causing the most trouble and possibly confine them to this one region to keep them from spreading.  The fences previously built could work however more natural 'barriers' should be researched and  implemented.  What should not be done is to introduce even more non-native species to the environment.  This will just cause a never ending chain of introducing invasive species to attempt to control the previous invasive species.