Is it possible to stop a cat allergy from developing in my son?

Sort of. The less exposure, the better. If he is genetically predisposed to develop a cat allergy, there is enough cat dander in the environment that he probably will. However, the more exposure he has, such as going for daycare in a home with cats, or - worse - bringing a cat into the home to live with him, the more likely he is to develop a cat allergy, and the worse the symptoms will become.