Nice little minigame!
I discovered on my own that we could move the bunny with arrow keys after shooting. It wasn't intuitive to me to try it but helped me get quite far, around 1500 before landing on a dreaded plant. I think some instructions explaining that we could move after shooting too would have made this clear.
Another improvement would be to make it clear how high the bunny is when it is off screen. It feels really random when it comes back down. It almost defeats allowing us to move it around, since we have no chance to know when it will come back down. I'm not familiar with the original game, so maybe that is just part of the chance.
The little characters are all quite charming, music and sounds have been chosen well too! Very cool little game! I had fun!