Good Morning, PPM! You are right to be concerned, especially with a child. I do not have any specific advice, but I will add my .02 worth.
A lot depends on the layout of your home. The reading I have done on home defense suggests having a "safe room" that everyone can get to quickly. You might want to consider creating one on each floor of your home. The door should have sturdy locks, have furniture or some type of protection you can use for cover, etc. Of course your child is your first concern, always. I will let those with children advise you on that.
I live alone so I understand your concern about being home alone with your child. I can only tell you what I do. First of all, I keep my doors locked all the time, unless I am outside working in the yard. I have a 55lb chocolate lab who will warn me if anyone is outside the house, day or night. I also have security lights, front and back. Motion detection lights would be better. You want to make your home as unattractive to a burgler as possible. I sleep with my .45 on the nightstand next to my bed. I am not paranoid, but I take reasonable precautions. If I ever come home and it's obvious that someone is inside or has been inside, I would leave and call the police. They are trained to clear a house or building and I am not. It's not worth my life to confront someone in my home.
Hope that helps a little. Good to see that you are concerned about these things and want to do some planning ahead. Oh, and welcome to the forum!