I assume you're looking into Carnival, when you refer to the 10 p.m. to 3 a.m. group babysitting? You have to decide whether your daughter would already be asleep at 10 p.m. (mine were at that age) and if so, whether you'd want to transfer her there at that hour.
Alternatively, Royal Carib. offers private, in cabin babysitting at all hours for an hourly fee. Also, they have Aqua Tots programming daily -- it's a 45 min. session w/a caregiver (your or your spouse) and features Fischer Price toys.
I think you'd be happy with either. Make sure you read "bringing the baby" and "what's there to do at sea w/kids under three" -- I wrote these articles and they're listed on the home page of the family cruise section.
Luisa Frey Gaynor
Family Cruise Editor