Couple of people have asked me about this, and I did a little research.

The quoted energy usage for early model reverse osmosis desalination plants is around 6 Watt-hours/litre. More modern plants appear to be more efficient and the quoted figures for WA and Vic are 4.1 and 4.6 respectively. A kilolitre of water costs around $1.

Assuming a modern shower head using 9 litres/minute and a 5 minute shower, the energy cost of a 45 litre shower using desalinated water is around 200-250 Watt hours. [In Vic that is about 240-300 gm CO2.]

But think for a moment about the cost of heating the water. Most people shower in water at around 43 degrees C, which is around 30 degrees above the temperature of cold water. It costs 4200 Joules to heat 1 litre of water by
1 degree C and 1 Watt hour is 3600 Joules. Putting the numbers together you get 45 * 30 * 4200 / 3600 = 1575 Watt hours (1800 gm CO2). Boiling water is around 3 times the energy cost.

So before you complain too loudly about the cost of desalination, remember that heating water for your shower costs roughly 6 times as much energy as desalinating the water.