While cats and babies can live together happily, some preparation is needed to ensure everything runs smoothly. Just as you prepare the house for your new baby, it is essential to prepare your cat for the upcoming changes as well. There should be no cats in the bedrooms of babies or young children. By young children, I mean children under the age of 4, and certainly do not put a cat near a sleeping baby. A cat sleeping close to a small baby poses a danger, even though I've only found one suspected case where a cat smothered a baby.