Herpes?

Okay so my SO gets cold sores every now and then. If he doesn’t have an active outbreak can I still get genital herpes if he does oral on me? I’m pregnant and so I’m being paranoid that I could have herpes which he hasn’t done oral in months since I found out and I haven’t had any signs I don’t think. I just don’t want to pass it to the baby. What are the chances of this happening? Also, when the baby is born do I need to take precautions with my SO and the baby since he is a carrier even if he doesn’t have an active outbreak? Sorry I’m a first time mom. I just want to make sure the baby is healthy in any possible.