How likely would my baby have a peanut allergy if his father has peanut allergy?

Higher than average. The chances of your baby developing peanut allergy are higher if there is a family history of peanut allergy. (exactly how much higher is not known.) until recently, experts recommended delaying introduction of peanuts and peanut products into the diets of children with a family history of peanut allergy until age 3, but recent studies suggest that this delay does not help prevent peanut allergy.
Higher. Yes, the risk is higher, but there is new evidence saying that trying it early may be protective in developing this allergy. I recommend talking to your pediatrician about how to do this safely.