You can clone the drive, but I can think of good reasons not to go this
route. If your computer is the standard setup with Linux on one partition,
now would be a good time to make three partitions, a small one for swap (not
to exceed twice your RAM), a larger one for / or root (which is where Ubuntu
goes, 8 -20 GBs depending on space available and your habits) and the
largest one fore /home (where your user data goes). If you already have this
setup then try cloning, but I find there is nothing like starting with a
clean slate. Any problems that you encounter on new hardware are easier to
diagnose. The other way you will wonder if you imported problems from
settings meant to work on different hardware.

A fresh installation need not be hard if you: 1) save your sources list if
you have outside repositories enabled 2) create a list of packages installed
and 3) back up your home folder to a usb dive or key. Then
post-installation, you just add the old sources to your new sources list,
install new packages based on the backup list (automatic with Synaptic or
apt-get; it just reads the text file and downloads new ones) and copy your
contents of the old home folder into the new one. If you have a slow
internet connection then you can use aptoncd to save your existing packages
to a CD or DVD then re-install from there.