I'm righty but left eye dominant. Long guns and bows I shoot left handed. Pistols right handed, which is easy with the isosceles stance. I think go with the eyes and the natural inclination of the child. Either way there are plenty of options. If there were a kid who just did not have a preference, leaning toward right handed shooting would yield a slight benefit. Either way, not a big deal.
It's good to practice shooting firearms with the off hand, IMO. This is especially true for tree stand hunting in heavy cover. I think it's also necessary to practice with the weak hand for defensive handgun shooting.
Lots of fun to be had with either choice.
