Hi Cookies and welcome to Cruise Chat.
Some cruise lines have special pricing for children; Royal Caribbean is not one of them. Royal Caribbean charges a reduced rate for the third and fourth person in your cabin, no matter what the age, even babies. So the third-person rate is lower than the first and second persons' rate, but is the same rate whether that third person is 2 or 102.
Royal Caribbean does have minimum age restrictions on their ships. I think in the Caribbean, babies have to be at least 6 months old to cruise. The age is higher, probably a minimum age of 1 year, in the Mediterranean and other itineraries.