I feel my feedback is very similar to the others, the cat sprite is great and the idea is really cute, but the gameplay needs refinement.
If we assume the goal of the game is to knock the objects off the shelf as I assume is intended, it might be good idea to make it so objects slowly get spawned in (if you want to get really fancy have an animation of a person putting them back on the shelf) and then give the player points based on how quickly they can knock them off again. Combine this with something similar to Sam's idea for movement where a tap moves the cat along and a hold swipes, as well as your cute sprites, and you've got the basis of a really nice cat-them-up.
That's obviously only one option, keep experimenting!