You should be able to right-click (or ctrl + left-click if right-click isn't turned on in the macOS settings) on a folder and choose "copy". Then, go in the folder you want to copy to, right-click in a blank spot in the right-hand pane and choose "paste". Or, if you want to move instead of copy, choose "cut".
Dragging and dropping should work for moving too. Just note that the "Speed dial" folder can only have one subfolders. So, you can drag a folder, hover over "Speed dial" in the left-hand pane and release, but you can't hover over a subfolder in "Speed dial" and drop a folder in to that subfolder.
