Got to agree with bacovel, controls leave a bit to be desired. Would also suggest a bit more response on the stopping. The jump also doesn't seem high enough by itself to reach the next level. The double jump is not apparent unless you experiment.
It was also extremely jarring from a player perspective to be instantly teleported to the bottom of the screen for the next level. If the level design remains persistent, recommend not resetting the player position at all. Alternatively, if you do reset it, add a fade out fade in transition effect (make sure to pause the game elements that aren't the fader so the player doesn't take damage until it fades in.
Overall, good effort for a first release game, lots of potential