I am making a graduation cap cake. I plan on placing a non edible square on top of the hat so that it will not melt in the car. First what do I use for the top of the hat and how do I place it on there without the icing peeling off when the top is removed when it is ready to eat??? HELP!

Use some cardboard for the top and cover in fondant on both sides. as for the icing peeling off, I am sure a bit would peel off - no big deal.