I looked it up, and the most common ingredient in many bug repellants is called "DEET". Some articles and studies say that it is okay, and others say it isn't (no studies have reported any harm to babies, just in animals) so I would advise against using products that contain DEET.
However, there are natural bug repellants that are fine to use. Some of them contain citronella, eucalyptus, and other natural repellants that are safe. I don't know if you have any near you, but Burts Bees sells an all natural repellant that is safe to use. Other than that, I would recommend Avon Skin So Soft OIL...in the original scent. Don't use the Skin So Soft repellants, or the other scents of their lotions. You want the original Skin So Soft oil formula. You can also burn citronella candles/torches in the yard when you are outside to repel bugs.
Hope that helps some...