I know this incident scared you, and it would scare me, too! Honestly, I'm not surprised that your dog snapped at the baby when the baby woke him up. The baby startled the dog. If the dog wanted to bite the baby, that would have happened.
I agree with the above poster that dogs react different to members of the family pack versus outsiders. Your child is still so young, and vulnerable. I'll bet he'd come around and be a huge protector.
That said, I don't trust my dog or any dog around an infant. I'd never leave him alone with your baby at all. It's inconvenient, but doable. Right now I've got a 2 month old and a dog and I live on the 3rd floor of a condo. Taking that dog out 3-4x per day with baby is SO INCONVENIENT!
That said, I'm doing it. I think you can probably resolve this with some extra effort and diligence. Best of luck to you.