Skype has long been a desktop (and mobile) app, but today it's available in your browser in the form of a new public beta. Unfortunately, Australians can't yet take advantage.
Right now, the beta is only available in the US and UK. We didn't have any luck getting it to work in Australia by tweaking browser or region settings, but your mileage may differ.
It's pretty similar to the mobile app — you can make calls, have text conversations, search through conversations, and everything's synced up between your various devices. It's a simple layout without a lot to it, but it works pretty well.