Many cruise lines have limits on the age a child can be before they can travel. Based on my experience, it is common for babies to be at least six months old on date of embarkation before they can cruise. It can differ based on where you are going too. So check on both issues with your preferred cruise company.
Most also have rules that do not allow children under the age of 18 or 16 to travel together in a cabin without an adult being present too. So if you are planning to book one cabin for your children under this age to share, you may be disappointed. The rules may differ for interconnecting cabins and vary by line and so double check, especially if booking via an agent. If booking direct either online or by phone the cruise line systems will usually reject bookings when all travellers in the cabin are under the required age.
Although many cruise lines are trying to attract families with children to travel with them, there are various rules and requirements about ages and who can share cabins. So check carefully that your family and travel preferences fit with the line you travel with.