To get the Doodle Hoverboard, you are going to need to be in Hardcore Mode at the very least. After that you need to be in the Doodle World area and unlock the Secret Barn area. Head into the Barn and look for the ladder with the hay behind it. If you look behind the hay, you will find the Doodle Hoverboard!
Remember, you have to be in HARDCORE MODE to find it!