It's tricky to keep a pet around a newborn, bercause beleive it or not, pets do get jealous.
However you are the one who knows your cat's temperament.
Of course there are things you can do such as:
always cutting the nails (one or twice per week)
Putting the cat in a closed room at night (such as the kitchen or the balcony if it has glass walls)
in regards of health issues there is nothing you need to worry about with your baby since you passed on your immunity to them