Pamina, don't know if you're still reading, but I am allergic to cats and if your child is allergic to them I suggest you find them a new home. Being allergic makes you miserable! If I go to anyone's home for the first time I will always ask if they have a cat so I can dose myself up with antihistamine/ventolin inhaler and I have to sit by an open window. Cat hair gets everywhere and not being in the room with a cat makes no difference. It makes your skin itch, your throat (inside) and scalp itch, you wheeze (like breathing through a straw), itchy eyes, runny nose and if I have been somewhere that has a cat and I didn't and had no medication, I still feel the effects two days later.
So I'm sure you'll know pretty quickly if the baby is allergic! Good Luck!