I wouldn't clone the same drive that you're booted up to. It may or may not even let you, but if it does, you run the risk of getting a corrupted image, because you're making an image of a "live" OS, and there's a good chance you'll run into "open file" issues, i.e. it can't copy a file that is open, and may either crash when it tries or create an incomplete/corrupted image. I mean, you can try, but you do run that risk. Personally I wouldn't want to start fresh on a new hard drive with an OS that was put in place that way.
Do you have the OS reinstall media? The better way is to simply boot from the media and install the OS onto the new drive (whether it's internal or external at that point doesn't matter), and then when it asks whether or not you're upgrading from another Mac, you can point it to the files on the old drive (assuming the OS you're using is new enough to have that feature).