I'm sure if you can find a suitcase you can fit it in, and just remove any heavy components from inside like PCI-E devices, and put them in something else, you could transport it without much issue, though you'd get some funny looks when it goes through scanners.
I've never flown, so I don't know much, but I'd assume doing something like that, would work.
Or you could ship your PC via Fedex or someone like that to your address there.
I wouldn't trust the luggage carriers of an airport with my Desktop. At the very least the case will probably be damaged. You are better off shipping it.
I would ship it UPS or Fedex. They will be cheaper, probably treat your box better than the airport treats luggage, you won't have to deal with moving it yourself, and airlines lose luggage a lot. I would go as far as to remove everything. take out the gpu, the cpu heatsink, take out your hdds, even remove the motherboard. Wrap them up in bubble wrap and packing foam and secure them all individually. UPS/FedEx WILL throw your computer's box, they WILL drop it from 5 feet in the air, WILL throw it into a truck unsecured. Even a drop can crack your mobo if it hits wrong. It's probably a bit extreme, but UPS and Fedex won't replace your expensive computer parts after they break them.
Honestly, I would just ship it. To save on cost you might even want to just ditch the case and ship the components and when you're in Japan order a new (smaller) case. Best of luck on your travels!