It should run fine. I ran FCE on my old dual-G4 (2x1Ghz) with 1gig of ram, and it worked fine. You may be crunched for screen real-estate on a MacBook, but of course you always have the option of expanding your desktop when you are home by using an external monitor.
Note that if you do High-def movie editing, you will be on the low-end of the requirements for the RAM. Apple says it needs 1 GB RAM for high-def, but 2 is preferable. But for regular stuff, 1 Gig should be a great start (you still may want more as you go along).