Let her experiment a bit more before making a decision. She is young and as a new shooter can learn to shoot lefty without the transition an entrenched older shooter would have. I may have missed if you are having her shoot irons and scope.

Two things to consider: My sister in law is left eye dominant, right handed. She had not shot much and had been taught by a guy who was not paying attention before she came to visit prior to a deer hunt. She mounted a rifle to her right shoulder and laid her right cheek over the comb to look through the scope with her left eye. I asked her if that was how she normally shot. Yes that was how she had been shooting, mostly a shotgun. All I could think was "Wow that must hurt!" With her cheekbone on top of the stock, the recoil would have been slamming her right under her eye. I might add she is tough as nails. She also did not know any different/better.

Then and there we converted her to shooting left handed so she could properly shoot with her left eye. She ended up with a right hand rifle but deals with it fine.

For me it is different. I have no dominant eye and am pretty ambidextrous. With a handgun I can actually shoot right eye-right hand or left eye-left hand. I could probably shoot a long gun either handed, but because I learned right handed, lefty is awkward. But, because I have no real dominant eye, I have to close one to aim. I find that the eye "obstructed" by the gun and sights or scope is over-ridden by the eye with unobstructed vision. That makes it difficult to aim with sights or a crosshair if I don't close the off-eye. I am not sure, but I think a person left eye dominant trying to shoot right handed might have the same problem with trying to keep their dominant eye open and still actually aim with their non-dominant eye.

For a kid, I vote go with the dominant eye.

Another thing to consider, I think you mentioned that her needing to shoot lefty was problematic because all your rifles are right hand. If you want and expect her to enjoy shooting, get her her own rifle. She needs something to fit her. That includes size and handedness. Most women and girls are forced to struggle with stocks that are too long. Being of smaller stature, I can vouch for the fact that groups can be immediately improved if the length of pull is altered to fit the shooter. Aiming is much more difficult when you can't ever see out of the whole field of view of a scope. A novice shooter may assume this is "normal" and not tell you they are having this problem. Another consideration is that most women have smaller faces, and so the comb height to scope height proportion can be a problem. This would be magnified in a 9 year old kid, girl or boy. What happens with that (personal observation due to my own size) is that you have to raise your head and not get much of a cheek weld on the stock because you can only look out the bottom half of a too-high scope with proper cheek positioning. FOr me certain stocks work, and others don't. Getting a stock comb riser (elastic with varying thicknesses of foam) can also solve this problem without a permanent change to a stock.

Progressive fitting as she learns and improves could pay dividends in her success, your pleasure, and having her join the ranks of active shooters.