Your question has been pretty much answered by other respondents, but
I'll make a couple of summary notes, because what you're asking, and
what you want are a little different.
Ed Mullen noted how you can move the Firefox binaries to another
location, by uninstalling, and when you reinstall, choosing a different
location to install to. However, the Firefox program itself doesn't
take up a lot of space, and moving won't do much to fix your disk space
issues, unless you're doing that with nearly all your applications.
Uninstall won't change your user profile, unless you explicitly allow
the uninstall to purge your profile data, and I don't think you want
that, at this stage.
For best space usage, s|b suggested moving your entire user profile to
another location, and that will give you the best improvement, because
that contains both your bookmarks and your browser cache. I agree with
the suggestion of MozBackup, because it's good for doing this kind of
thing, and in this context, is a little easier than poking with editing
your profiles.ini file and digging into the windows %APPDATA% directory
to find the raw data. And it will get everything in the profile,
including your bookmarks.
Jeff Barnett suggested moving the cache to another drive, and that's a
good suggestion, depending on how large your cache is. It might or
might not relieve space issues on the C: drive.
One other suggestion, whether you move the cache or not, you may want to
consider lowering the maximum size of the cache, and/or setting Firefox
to delete cache contents, when you exit. Depending on your usage, you
could find that having as much cached data won't affect performance, but
where the cache is taking up considerably less space.
Smith