I don't recall any card that allows you to control a ship without a bunny in it. If you can post the actual text from the card it would help. But I don't think it is possible to get a ship with no bunny to Jupiter.
There is a card in the red expansion called Bunny Headroom that allows you to control a bunnyless ship. I'd say that you can turn in your carrot markers at Jupiter when using Bunny Headroom.