I think this is a situation where things depend on the person and the only way to know is trial and error. I gave it some thought prior to posting this thread, and think the following reasoning is sound, but am open to having holes poked in it as I may be less informed than I think.I'm left eye dominant, right handed as well. I am super happy i did not learn to shoot lefty. Just teach her right, she'll adapt plenty fast and itll not even be a thought once she's an adult.
It barely matters in scoped rifles anyways. Pistols very much but a scoped rifle, nah.
There are degrees of eye dominance. I have watched my wife switch dominant eye twice in a single range session with a handgun (right to left and back to right when I asked why she was holding the gun funny).
But there are also people who report a very rapid improvement in shooting by switching to dominate eye after a lifetime of doing it another way, particularly bows and shotguns. There is also value in being able to use rifles with irons or red dots both eyes open and not having to close one eye for close range work in high stress situations.
There is always enough right handed gear around to make deciding to try switching to her dominant hand easy if eye dominance is not as significant for her. However, going the other way is much harder and if significant the struggle might be enough to turn her off from shooting (particularly her, with her personality).
Plus, even with a scope, why use the eye that doesn't see as well to aim (as is the case with her)?
So, at present I'm inclined to set her up to learn on the dominant eye as I judge (based on gestalt/SWAG) that it is most likely to be successful and have her wanting to shoot. And if she ends up not liking shooting at all, I will not be left wondering if my being cheap was to blame.