Nice start, but I'm not sure I like being unable to control trajectory midair. Maybe that's realistic, but then again, is realism what people really want in a game about a kitten fighting demons? I'm assuming it is a kitten because of its scale compared to the furniture and appliances.
Also I think there's too much waiting around/trial-and-error in the bathroom and first boss. Level Two is where I rage-quit, though I might have soldiered on if I had access to a controller. Still, in that level I noticed the cat falling through platform that was rising and lowering, so you might want to check collisions.
The in-level music is good but maybe there should be different songs for different levels. The boss music isn't exactly catchy but it fits.
