My son is right handed, left eye dominant. He does everything right handed, except shooting. Be it rifle, or bow, he shoots left handed. He still throws right handed, and writes right handed.
My son was born blind in his right eye, but is right handed. Handguns he shoots right-handed, but adjusts his head to use his left eye. Long guns and bows he shoots left handed. It was never really and issue for him, he mostly figured out the way that worked best for him with a little guidance from me. At six, he should be able to adapt pretty easily.