Mister30, good to hear she's running again.
Should be able to truck a car from Melb to Alice for about $1200. Call a few truck companies as the price does vary a lot, some try to charge up to $3000. The train is very expensive and not insured for damages in transit.
www.cevacarcarrying.com.au -- this is who I used..
www.auto-logistics.com.au
http://www.movingcars.com.au/ -- this mob jerked me around.
search google for more if you want. There are heaps.