I also recommend either SuperDuper (which I use) or Carbon Copy Cloner.
While Time Machine is great for maintaining a continuous backup or your files, it is not the choice for the OP's current needs. SD and CCC can create a true bootable clone.
After creating a clone with either, I highly recommend that you reboot your computer to test the clone. You do this by holding down the Option key as soon as you hear the boot tone. After the initial portion of the boot cycle you will get a sceen allowing you to select the desired boot volumn from any and all bootable volumns. Pick the new clone and confirm that all is good. You can then shutdown, disconnect the clone for safety, and reboot again.
If the subsequent OS upgrade fails or proves undesireable, you can boot from the clone and have a working, but likely slower, system right away by doing the Option key thing at boot time. Once you've booted using the clone, its a simple matter to re-clone it back onto the internal drive.
Since the OP's external is 2tb and the internal is 1tb, I would suggest that the external be repartitioned using Disk Utility first. That way it can hold two clones, one done before upgrade and one after.