Australia is probably the best country in the world to safely store nuclear waste. Sparse population, and almost no tectonic movement. It already has areas which are radioactive too (from historical nuclear testing)
Australia is also currently in the beginning stages of a major energy crisis, which is partly caused by Japan (Some background, Australia signed a major LPG export agreement that intended to fulfill using coal stem gas reserves. When these reserves didn't deliver the quantities required, they instead raided the local domestic supply). You can currently purchase Australian gas in Japan for less than you can in Australia.
So Japan could directly contribute to Australia's immediate and long term energy security, in exchange for nuclear waste storage.