Double occupancy means the price is for two persons, minimum of 2-persons in the room. In other words, if a single person wanted a room for themselves alone, they would have to pay as much as if 2-people were in the room.
You and the child would be two people, so effectively you would be using an adult's points for the child.
Right now, there is a special on for selected dates in September, November, and December. Cat. 10 or 11 inside stateroom is 106 points per person. Thus for two of you it would be 212 points.
This is for the 7-day cruise. Check your latest issue of VM, pg 3 for details.
If you had someone else join you, using the 106 points for them, then the child would be 53 points, or a total of 265 points for three persons.
Hope this helps. I don't know what 3 or 4 day cruises would be. You can call Disney to find out.
Caskbill