The correct answer is .... it depends!
It depends on which source you read, apparently.
|Year Book of Australia (1978)||36 735 km|
|Australian Encyclopedia||19 658 km|
|Australian Handbook||19 320 km|
So who is correct? The answer is: all of them! Each source used a ruler with different sized increments on it. If you measure the coastline with a ruler that is just 1 mm long, you would get a length of 132 000 km!
The article on the next page is taken from The Australian Geographer, 1979 and discusses this problem in a little more detail.