Here is my easy way to make the pocket for the bunny. It is so simple, but I didn't want a lot of mechanism on the card ruining the "magic".
I used tear tape on the sides of the table/cake stand and folded a rectangular piece of cardstock in half. Then, I put tear tap on both sides of it.
Next, I adhered it to the bottom of the "table" and removed the backing from the next three pieces of tear tape.
Then, I adhered it to the card centered above the "table base". The bunny looks like this before you add the magical hat.
Because it is such a close fit, the hat is only adhered to the table, so it is really easy to remove the bunny. However, I can turn it upside down, and the bunny doesn't fall out.