Cool concept! It took me a long time to get through level 2 but I finally started to get the hang of it. But then level 3 was way too unforgiving with the very tiny landing area on the top surface. The timing of moving and dashing is quite difficult to get right. It might be nice to start out with easier levels and gradually increase difficulty (or I just suck at this game :D )
One thing that also messed me up was that the moving platforms seemed to be one-way only, which was counter intuitive -- I expected that I'd be able to land on either side of that platform.
I appreciate the heart you added in level 2 -- I needed it many times. If you take the game idea further, it might be nice to also have a special star item that makes the player invincible for a short time.