Most likely, you already know if your child is likely to get seasick.
If your child suffers from motion sickness on car trips, plane trips or amusement park rides, your child will probably suffer from motion sickness on the ship, especially if the seas are rough. I'd be especially careful if your child gets queasy in Imax movies, where the theater doesn't move, but the "flying" motions on the screen fool his/her inner ears into triggering nausea.
On the other hand, if your child never suffers queasiness under such conditions, it's unlikely (but still possible) that your child will feel motion sickness on the ship.
If anyone tells you, "only adults get seasick, kids don't," they haven't met my kids.
Also, be careful about advice on this board about giving Bonine (Meclizine) to children. Check with your doctor. According to the manufacturer, Pfizer, Inc., "Do not give to children under 12 years of age unless directed by a doctor." Our doctor said it was okay for us to give Bonine to our 10- and 12-year-old daugthers, but she "would not recommend it for 6-year-olds."
Also, be aware that Original Dramamine and Dramamine Less Drowsy Formula are two entirely different medications. Original Dramamine may be given to children. Dramamine Less Drowsy Formula is the same medication as Bonine, and thus should only be given to children is directed by a doctor.
For more on Bonine, see
http://www.acidrelief.com/conaffairs/acid_relief6.shtml