I am not sure your situation, but a child under 1 is very difficult to leave with someone you don't know in a room.
May I suggest taking someone in your room even a known teenage babysitter from home with you. For the 3/4th person on Royal Carribean it is only 299 on most ships. That is what i would do, we did this many years back, but my kids are now 3 and 11 and are old enough to go to the centers.
It just comes back to, how bad do you want to go?.