It should be about $1000 including upto $65,000 in insurance. Go to the website
www.movingcars.com.au, they use Ceva and are often cheaper than going to Ceva direct - who are the best. You only have to go through AQUIS when entering Tas, this does not cost anything anyway and they are only looking for fruit and veg that might contain Fruit Fly which is not in Tas. However, all cars and freight are often checked on departure for the illegal movement of firearms, drugs and dangerous goods such as gas bottles etc...
For Mini's, I think $1000 is good value when you factor in your time to drive it to Sydney, fuel and a real risk of a mechanical issue (especially if it is a hot mini).