µTorrent has a migration guide to do exactly this: https://documentation.help/uTorrent/Chapter03_02.html
As I understand it you can do it the easy way or the hard way (particularly hard if you have 1K torrents).
Easy way: if you keep your downloads folder path exactly the same (by making sure the external HDD gets the same drive letter on the new PC), you can copy your entire settings directory to the new PC and it should all just work.
Hard way: on the new PC, configure your completed downloads folder to point to the external HDD and then manually add all the .torrent files again. µTorrent should then see that the files are already there. If it doesn't you may need to tell µTorrent to recheck/rescan the torrent.
Good luck!