That was my exact reason for booking the nanny to begin with-- to have that built-in sitter so we could enjoy all the activities that babies were not suited for, only it didn't work out that way. My nanny had never sailed before, was elder and did not do well out at sea at all, so I became 'nanny' to the children, missed all shows and activities I had wanted to particpate in due to having an ill child and ill nanny and why I reference that cruise as my 'cruise from hell.' Live and learn. I often flew my mother in to stay with my babies, especially when they were under 2. My mother is an RN and would have known instantly that he had infantile roseola as all 4 of my siblings and I had it. The ship doctor had no clue what it was causing me to worry much more and I couldn't get off that ship fast enough to get him home to his regular doctor.
After that, I just left the babies at home with a nanny and mother until they reached 2 and were old enough to enter in programs on board. I love having my children on board with me, but I also need that necessary break from time-to-time, as any parent does, and why I do not recommend anyone ever booking a child under 2 without a nanny unless they have confirmed that their cruise line will accept babies under 2. I have heard of some accepting tips as someone posted above, but my experience was that was for late in the evening. Rules may have changed over the years as well.
My children are much older now so I don't have the stressors of worrying about that kind of thing anymore thank goodness.
Glad your experience with the nanny turned out much better than mine did.