Most of the desert islands don't have drinking water and we'll need to harvest serious amounts of rainwater there and/or use a seawater filter system (but those seem to be costly and spend a load of energy):
http://en.wikipedia.org/wiki/Solar_Powered_Desalination_Unit (these kinds at least would provide their own electricity needs and can surely be bought from Australia)
http://en.wikipedia.org/wiki/Reverse_osmosis
I do think we'd be able to manage without a seawater desalination unit provided that we bring a lot of drinking water with us and a lot of containers to help us harvest and store rainwater.. We'll probably have to make the final judgment about getting a seawater desalination unit only once we've bought the boat. Naturally it would be stupid to bring empty containers so we'd re-use our full water containers, barrels (much more efficient in harvesting) etc. We can also the islands' wood for harvesting rainwater...
It will probably be best that we don't drink straight from any of the big water containers we bring, so that they'd stay more clean.
We can also use Solar Stills. Especially bought, ready to use modern ones could be very useful. The ones we can make ourselves probably wouldn't suffice.
We should probably also bring a rainwater filtering unit of some sort, because rainwater isn't 100% clean even right when it comes down and while it is a lot cleaner where there's little to no pollution (like where we are going), I still think long-term we should filter or boil the rainwater.
Natural rainwater filtering: Filtering technologies have been used in the past and today to purify it by passing it through a series of rocks, gravels, and sands to scrub out contaminants. These methods have proven to be very effective.
