The cat is only obtainable through gambling when there is the event "The Gambler" that can trigger after Gustav comes to the fort. If you win the gambling three times in a row, he will say he doesn't have any more supplies to even feed his cat, so he gives it to you. You can count on the fact of winning her if you play repeatedly and you got enough food in stock.
Just as with dogs no cats can be exchanged with Gustav. Animals do not belong in his assortment.