Carnival and NCL are your two choices for a two year old and she must be two by the date of the sailing. We have used both cruise lines because of our daughters age and loved both children's programs. NCL used to be 3 yrs old but it changed last May 1st. Other lines are from 3 to 5 before the allow children in the program.
NCL will not change diapers so if your daughter is not fully potty trained they will give you a beeper and you must come change them. Carnival changes diapers and they also accept children under 2 for babysitting. NCL does not accept anyone under two for babysitting.
If you have more questions email me directly. My daughter will be sailing on her 6th cruise 14 days before her 4th birthday so I've done this a few times.