Yes, your W800i will work in Australia.
And yes, you need to have your current provider unlock it, which should be pretty simple. Once in Oz, you can get a local SIM card within minutes, even at the airport if you want. The pre-paid $50 plan from Vodafone is pretty great, IMHO.
And yes, all you need is a socket adapter for the charger to work there. Same goes for digital cameras, laptops, MP3 players, etc, as they all have built-in transformers in the AC adapters.