What is the cheapest way to get from Thailand to Australia with a car?

I can't tell you the absolute cheapest, but I can tell you it's not commonly done. It is however uncommonly done - by people on "adventure" trips, challenges, etc.

One current such adventure I could think of is "It's on the Meter - World Taxi Challenge". I had heard that they had travelled with their London Taxi from England to Australia so did some searching for how they got to Australia.

In a Wall Street Journal article linked from the Wikipedia page I found this line which may be of interest to you:

When they ran out of land between Singapore and Darwin, Australia, the cab was loaded onto a cargo ship at a cost of $3,000.

So I don't know whether you regard $3,000 as "cheap" or not. If you're on a weekend jaunt to Australia in some old banger then perhaps not, if you're fulfilling a childhood dream or drunken bet to drive to Australia in some bizarre or interesting jalopy and would be doing it anyway for the adventure, then perhaps this is a good ballpark figure.

If you want to bring it back here (to Thailand) you will almost certainly have to pay import tax on it (even if it was Thai to begin with). Prices hold very well here with secondary depreciation almost nil (primary depreciation is when it is first bought and goes from new to second hand - this is still low in Thailand) and prices hold for more than a decade easily on well maintained cars. Also, if it was a foreign model (i.e. not assembled in Thailand) then it would have had up to 400% import tax applied to its price when purchased.

All this means it will be cost effective to sell it here (Thailand) and buy again in Australia - you will probably be able to sell a reasonably new car (say 5 year old) and still make money after buying new in Australia (like for like models of course).

There is no ferry - it is half the globe away! Like a ferry to South Africa! Only way is to ship it.