To get your kitty first head to the Garden Gazebo. Look around and you will see rocks laying around. Walk through them. There are a total of 6. You must collect them all and they will form a cat statue.
Next make sure you have a bottle of mulch. To get that play the bounce game by clicking on the cat ( pictured above ) Next you will need to find the Garden Sprites. Which are flowers that are walking around. Click on the first one, which is red. They will turn your statue into a real cat. It will cost you some coins of course. 🙂