Backup your folder C:\Users\yourusername\Documents\My Games\GalCiv3\Designs

Once you got the new machine running, copy your designs from there into that folder of the new system. That should be all.

(edit: dunno if there's a diff location on other Winversions, I use Win 10)

You are likely to have a lot of files on your old machine that you want to move onto your new one. Windows, some time ago, started the convention of keeping personal files in C:\Users\<user name>\Documents and its sub-folders, and copying all files in that folder and its sub-folders from the old machine to the new one as part of the migration. Since your personal ship definitions are saved within this structure (...\Documents\My games\Galciv3\ and its sub-folders), along with your saved games and much more of your private GC3 stuff (this is also where you should have put any mods you may be using), you will find all of it on your new machine once you have followed this standard migration convention.

Be sure to learn how to make integrated Intel® HD Graphics 630 work best with your GTX 1060.

AND -- especially -- watch the heat carefully. Excess heat causes the CPU and/or GPUs to reduce clock speed. So far, GC3 has been less of a heat generator than Civ V and even some older but rebooted games I have played. So far, my impression is that the biggest cause of heat is graphics resolution.