I will be flying from Australia to Tokyo in a few weeks time and was wondering whether I am allowed to take my laptop there?
If your laptop is for personal or work use then, yes, you can bring it to Japan.
If you plan on selling the laptop, that would be a separate question.
Please note that you will likely need a plug adapter (not the same as a voltage converter) to charge your laptop in Japan. Japan delivers 100V electricity with a non-grounded U.S. style plug. More information here.
Your laptop's AC adapter will probably accept 100V electricity but you should read the label to confirm.