It's only good if you allowing them to be around the baby while it's sleeping because they smell the milk on their lips and try getting it. As long as you watch the cat and down allow the the cat to sleep in your room you will be fine.
They say it's not good to have cats around your baby. It's really dangerous.
Its been said that kids who grow up with pets are less likely to develop allergies to them ...now idk how accurate that is but we got pets when my first was like 2 months old and have had them ever since and she's just fine...I'm gunna go with its a 50/50 chance
The chances are very low. Allergies can be hereditary but sense no one else is the chances are very low. I have a cat and I am 36 weeks. My fiance and I aren't allergic neither are our other 2 kids.