I am planning to charge my phone and camera while in Japan and am wondering if I will need to purchase a power socket converter? Also, is the wattage in Japan the same as Australian power sockets?
The real problem here is the voltage, In Japan its 100V and in Australia it is 240V. Almost all phone, camera and laptop chargers are dual voltage and would work in any electricity from 100-240V but that's not the case for almost all other electrical devices. Make it a habit to read the label that shows the voltage information on the back of chargers and electrical devices before you plug your devices in a foreign country.
Since in Australia is 240V and in Japan is 100V then there will be no damage to your devices if you plug an Australian device in Japan even though it will not work. Anyway the opposite (if you plug a 100V device into 240V power socket) will lead to fireworks show so in case you are planning to buy electrical devices from Japan make sure it supports 240V.
There is an added complication with Australian -> Japanese power. Japanese outlets are not earthed. This can be a problem especially for laptop chargers, as many sold in Australia have a three pin plug.
You could buy a new power brick, but they are a little expensive. I found this guy (see pic) at Bic Camera (a consumer electronics chain), and It worked perfectly without the earth connected.
Of course, the earth is there for a reason, and this adapter sacrifices on safety. I am not so much recommending this method as describing my solution.
The other option with some appliances is simply to buy a new one. My wife ended up buying a hair-straightener in Japan anyway, as the 240V Australian one didn't heat up on Japanese power. Those kind of small appliances are cheap there anyway.
TL;DR Check that the appliances you bring are two-pin.