No, do not re-import your images. I assume you can see the thumbnails in the library module, just cannot access the full images, right? If this is the case there should be an exclamation mark in the top right corner of every one of your pictures and you only have to tell LR where the images are now.
Click the exclamation mark of one of the images and a dialog window should pop-up, telling you that LR cannot find the file, but with an option to locate it. Press "Locate" and navigate to the folder on your new HD where the file is. If in the new external HD you kept the same folder structure that you had on the internal disk, LR will be able to find all your images and re-link them to the database without further intervention.