I also have a eeePC that I use to review RevTK with sometimes. I bought mine with an English version of the OS because I'm the only one in my household that can read Japanese... but, if you're decent with computers, you should be able to install SCIM-anthy on it, which is basically a linux version of the Windows IME language bar thing. SCIM came installed on mine (for switching between European languages), but anthy is the way to go for inputting Japanese text.
I seem to recall the eeePC forums had some decent posts about installing Japanese input, so if you wade through all the garbage posts until you find one that talks about SCIM-anthy, then you should be good. AH hell... <greps the internet a bit> Here's the post:
http://forum.eeeuser.com/viewtopic.php?pid=33458#p33458
follow his instructions (I think they are pretty noob-friendly, for those who don't heart teh linux), and you should be good. You want to use the "anthy" package for SCIM because it *doesn't* suck. It pretty perfectly mimicks the way that Japanese windows lets you type... you can switch Jgo input on and off with quick key combos, and you can type a whole sentence out before you decide to change the kana to kanji.
Some of the other SCIM packages are total ass and make you change kana to kanji before you move on to a new word, which is *incredibly* frustrating, time consuming, and not at all how Real Live Japanese People type in their language. I think you can also turn on kana touch typing (so that you don't type in romaji), but with an english keyboard you'd need to memorize where the kana keys were located. *shrug*
Anyway, I've installed Jgo support successfully (actually, twice, due to a complication with a different program install job that I horrifically botched), so feel free to send questions my way.
-ang