Ginger works wonders for motion sickness. I personally get very bad motion sickness (it is usually due to fluid in the ears or an inner ear imbalance), and used to have to take Dromomine. When I was pregnant that wasn't an option and I took ginger capsules instead-- worked like a charm. I also used a bit of pressure on my wrist points-- here is a picture showing where to press for a few minutes: http://wakowa.files.wordpress.com/2007/07/p6_point.jpg
There is nothing harmful with ginger, in fact it is quite good for you, however it does burn a bit. I wouldn't recommend the capsules for a baby or young child because they'd be too strong. You might try brewing some ginger tea and diluting that in a bottle or sippy cup. You can get ginger tea bags from many stores, esp. health stores, or you can just get fresh ginger root (my preference) from the produce section of most grocery stores and you can grate that into a pot of boiling drinking water. Let it brew until it starts to smell/change color a bit and then just sift off the solids and you'll have a (imo) delicious and very effective home remedy.... Remember to dilute for a little one though :-)
Best of luck to you and yours.
NOTE: I did just find this article on medicinal uses of ginger: http://www.umm.edu/altmed/articles/ginger-000246.htm It recommends not using ginger for kids under 2 years old. You might want to check with your doctor or a midwife/herbalist just to be safe!