After reading these posts, I guess it is a split decision on the newborn. Personally I would leave the baby home with grandma. You'll get very little time alone for the next 18 years or so. Also, the germs that float around a cruise ship may not be healty for a baby.
When my children were younger and we took them to Disney World it was nuts. As they got older and could off on their own, my DH and I would sit on Main Street and people watch. The funniest sites were 1.) worn out parents with small, crying, whiny children at 11:00 in the morning 2.) parents yelling at the small, crying, whiny kids because they didn't want a picture with Mickey or other characters. One child went so far as to plunk himself on the ground and refuse to move. We thought it was funny but the parents were on the verge of a nervous breakdown. What a long day they were in for. My thoughts, what a way to "VACATION".
I'm not saying small children don't belong at Disney or on a cruise but be prepared for the worst. I work with kids all day and they are very unpredictable. The best behaved child can turn into a nightmare very quickly and for no apparent reason. Especially if they know they will have an audience. I know that your child is a newborn, although you don't say how old, but they can cry to the point of making others crazy, mostly people who don't have children or who haven't been around kids in a while. I would really give some thought to taking the newborn. Whatever your decision, have a great cruise.