Glad to hear you're considering cruise with your infant. If you are planning on cruising with RCCL, however, the babysitting doesn't start until infants are one year old...
However, why don't you consider Disney Cruise Line? We cruised on DCL when my son was 7 months and enrolled him in the nursery for a number of times during our cruise. This is the only cruise line with nurseries for infants and toddlers. While you must pay an hourly fee, the personnel in the nursery were great. See my article on Disney's nursery posted on this section of the web site. There's also an article called "Bringing the baby" posted there which is general tips on cruising with a little one.
Let me know what you decide.
Luisa Frey Gaynor
Family Cruise Editor