The only possible issue is that the latest version of Firefox may not support 10.3, you may have to use an older version which then doesn't support the new database based goodness of Firefox bookmarks and whatnot.
You'll need to figure out just what versions of Mac OS X are supported by what versions of Firefox. Ultimately I suppose it can't hurt to try moving your profile, but be prepared for the possibility that you'll just have to start fresh.
I use the latest version of Firefox on an XP machine. I want to transfer my Firefox bookmarks, profile, etc. to a machine running Mac OS 10.3
Are there any snags to look out for since Mac OS 10.3 is a somewhat older operating system?