You also have to be careful if the cat scratches or bites as it can give you toxoplasmosis or listeriosis which can cause miscarriage and still birth or severe defects. Even death in newborns
Unless the cat is like infected with ringworm then you should be alright. Just don't clean the litter box, but if you must wear gloves, like those yellow ones, and a face mask. And then wash really good with soap and warm water.
Not necessarily . but u can be careful. Like if the baby is sleeping then make sure the cat can't get in the room.. Or just keep a close eye to make sure the cat doesn't get on the babies face or start licking the babies face.