Like the theme parks, both Disney ships are geared toward kids. But, like the theme parks, there is plenty for adults if you know where to look. At 15 months, there won't be any organized activities for your son but there is a great nursery to - ahem - dump him. You get a pager so you never feel out of touch, even if you go ashore.
During the day I'll bet the three of you have a great time, but you might want to duck into the ESPN sports bar in the stack between the pools for whatever. There are three pools, kids, accompanied by family, family and adult. The ship is fitted with a next century sound system so the backgound music matches the setting.
The early sitting is nearly all the families with small children, the late seating is really late - 8:30. If you want to feed him early, great chance for the two of you to enjoy dinner. You will have to collect him by about 1am as I recall.
There is an adults only section of one of the decks forward. Three nightclubs that range from serene to raucous. The movie is G rated Disney until about 11 when the R rated stuff is shown. Floor show has lots of action, lights and noise (music) that he might enjoy. Unless he really likes being lugged around by you, doubt if he will enjoy going ashore. You can be quite confident leaving him on the ship. The staff (counselors) aboard just for entertaining the kids is extensive and exceptionally competent. There is a problem with the older kids preferring to be with the group than with parents.