Great concept and although the art is simple and childish, it has a certain charm to it.
However, the out of control nature of the gun has no impact on the gameplay except for defeating the boss. When every obstacle can simply be jumped over, the gun becomes unnecessary. Perhaps doors to shoot down or enemies which can't be vaulted over whould have made the gun more important to the gameplay.
Also, the boss seemed a little unfair with no way to predict the platforms to avoid its attacks. Maybe that's what you were going for but it just seemed a little cruel.
Other than that, I still played it and enjoyed it!