A.T.
This is only my immediate gut reaction to your concerns...DO NOT get a "certain type" of dog. I do not know what kind it is...but, I can only imagine if your house insurance may be yanked??? Do not do this to your child, there are too many horror stories out there about the dogs turning on their own families. If that should happen, not only will you be liable but any fears you had before would seem minimal.
I would think that the cost of a home security system would be cheaper in the long run that losing or having your homeowner's insurance go up.
Is it possible for you to live in a condominium? Or a townhome? Maybe that would help you feel more secure, do you have a close friend that could benefit living with you and paying rent? Are you in the type of neighborhood where you don't feel safe?
I feel for you, I hope that you are able to find some reassurance soon. But, please don't risk your life or your child's life with certain type of dogs.
Please update soon, I would love to hear how you are doing! You are in my prayers.