I'm right handed, strong left eye dominant.
Grandpa was ex US Navy and taught us to shoot open sights with both eyes open.
I couldn't hit the braod side of the barn, from inside the barn, trying to keep both eyes open and shooting right handed with the Model 69A.
Once he realized I was canting my head over the stock to use my left eye and keep both eyes open, he had me switch to shooting left handed. Much better results. Never looked back. Many of the rifles I liked using more as a kid shooting only open sights were the lever action rifles. Never shot a scoped rifles until I was in my 20's.
Of course, most of my bolts were right handed, until I could start to afford better quality firearms, and/or able to find left handed Remington 700's (and other makes later on; Ruger, Browning, Sako, etc.). Today, almost all of my bolt action rifles are lh.
Getting into archery, it was left handed from the very beginning, with both traditional and compound bows. As a bow technician, I had to learn to shoot right handed in order to set up and tune bows. This forced me to be very conscious and consistent in my shooting form, although I must close my left eye first to gain right eye dominance, then learned to maintain that dominance when I open my left eye and still shoot right handed with both eyes open; this skill takes a lot of focus and time to acquire, and maintain. Have also trained myself to do this with rifles, in the event I ever have to shoot right handed due to circumstances or injury when afield.
As your daughter is young, set her up to win by getting her left handed firearms and bows. She will do better, quicker, and have more fun because of it. This will increase her level of enjoyment and ongoing participation.
Teaching to to shoot right handed later, after she has mastered her left handed skills, will add to her ability and overall skill level. She may also like the added challenge of being able to master a skill that most people cannot (or are willing to try) do.