It sounds like you have the right idea. I would suggest you do this from a live CD (if you installed from the live CD, that will work fine) to make sure nothing changes as you do the copying. Since you're copying to a blank partition, there is no reason to force (-f) anything, but you should use
-a (archive) with your
cp command instead of simply
-r so you preserve ownership/permissions/symlinks. I am not sure what your UID question is, but the UUID is generated when you create a filesystem. If/when you run any of the "make filesystem" commands (such as
mkfs.ext3), you will get a new UUID.
EDIT: Make sure you keep you original disks intact until you are sure you have the system running properly with the new disk.