For the copying you need of course some sort of life system (rescue or whatever), because you can must have your root file system unmounted when copying. Your assumption about that is correct.
You should not forget to check (and change) every configuration place where your partition is mentioned, like /etc/fstab and in Grub. It depends on what identification is used there (/dev/disk/by-*), but it is very likely to be changed except wen you use by-label or by-uuid and cloned).