If you are running iMovie HD just hit export full quality. It will output a rather large DV file that FCP won't have a problem with. Sounds to me like you are trying to export to a Quicktime DV stream. That will kill the quality like you say.
Here's what I'd do. You have an FCP license which means it came with Quicktime pro. Open your high quality .mov with QTP and go to file export. Save as quicktime mov but hit options. Go to settings and change the compression type to DV/DVCPRO NTSC. Rack the data rate higher than the default 3000 Kb/sec. How high depends on the length of the video. This should give you a high quality DV file that FCP can read.
If you're running iMovie 09 and you're just doing simple cuts, I'd say don't even bother with FCP. A lot of simple broadcast productions I've worked on have been literally slapped together in iMovie. Shocking but hey, it works. Plus you have the convenience of direct upload to Youtube and mobileme. Media browser is cool too, especially if you score with Garageband.