You can click on the "My stuff" tab in the middle of the learntomod homepage, then scroll down until you see worlds. You'll see a list of worlds you've downloaded on learntomod. Click view on the newest / latest world then click the zip file backup button.
All the worlds on learntomod are meant to be played on multiplayer type worlds, so I'm not sure your world will work on singleplayer. But it's worth trying,