You don't have to copy the save file, they are kept at User/APP Data/ Local/ TheArkGame/Saved/SaveGames
When you download a new version, simply just open the game and it will load your file. Please bare in mind that Prologue version are a different instance with Patreon release so your save file for Prologue won't be read in the Patreon version.
We will include updater for more convenience in the future.
Thanks