Baby and coldsore? Very worried

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Hello
My husband had kissed, cuddled and snuggled into our daughter yesterday evening who is 5 and a half months. 6 months on 11th of April. Within an hour he felt his lip itch and burn and by the looks of it this morning he has a coldsore coming up. It’s became red and little tiny blisters visible around 1 big red bump and it’s still itchy. 
I am quite paranoid about health in general especially the baby’s health. 
Will she be ok? What’s chances of her getting virus from him? 
He’ll not be holding or feeding her till it’s cleared which we both agreed is best idea and may sound over dramatic to some but for my anxiety and baby’s safety that’s what we feel is best. 
I am looking for some advice, reassurance or something whose had the same problem