P.
I know animals are hard work, but they are not disposable. When you make that choice to welcome a cat or dog into your home, it is a commitment you take on for the animals life span. So now you have a newborn and suddenly the cats are inconvenient? I have two dogs and two cats. I didn't get rid of them when my daughter was born. Is it more work? Of course! Have you tried brushing your cats to keep the shedding at a minimum? Have you tried switching their diets so they don't vomit?
It sounds like you are being way too overprotective about your baby and keeping the cats away from her. My daughter was around all of our animals since the day she was brought home from the hospital. She crawled on the floor, played with them, and now, she holds them and loves them. Having animals in the house teaches your child valuable lessons, one of them being compassion. Keep your cats. Your baby will love them when she gets a little older.