Books don't support operating systems; reader software supports books.
A quick look at the
fbreader website shows me that fbreader supports epub, which seems to be developing into the industry standard. Since with calibre virtually any accessible format can be an epub within seconds, you're good there.
I'm not sure what you mean by "most of your books" -- you mean the ebooks on MobileRead? They're separated by format, so you just need to see which formats the books you're interested in come in, and convert them if they're not the one you want.
Which ASUS netbook do you have, by the way? I've got a 901, which doesn't have fbreader (though apparently a previous version of its particularly strange OS/app package did), and I have a certain degree of paranoia when it comes to trying to install anything on that odd little computer. The process isn't like anything I'm familiar with, and as much as I like the convenience of its simple function-oriented UI on top of some kind of mutant Xandros, I'm getting seriously tempted to throw some other distro on there just so I can actually install stuff that works. It's a very bizarre feeling to have a Linux machine over which I have less control than Windows. Also, the fact that ASUS's "software" source is 99% links to random unrelated websites pisses me off. I love my "kneetop", as I call it, but I really want to grab someone at ASUS by the throat and shake hard.