Unable to make a recommendation on a low end red dot, but can give you some first hand advice on what to look for based on my daughter's experience, combined with my training and experience on high end red dots.
My daughter is currently a well seasoned wing shooter with a taste for nice doubles. She started off as a child right handed with a left eye dominance, though it was not overly strong. She was helped by the late Tom Knapp with the use of a Swedish invention for shotgunners having cross eye dominance. It was eventually marketed in the US. The concept is simple, and it is the same in how a little Trijicon T2 works so well:
The idea is you want to shoot with both eyes open, with most of what you see of the target not being obstructed by the sight, yet, only the sighting eye can see the dot. Your brain puts the image together, and the dot floats over the image without double vision.
The Swedish device was a fiber optic rod, recessed within an aluminum tube, mounted over the front bead. From the sighting eye it was no larger than a bead, but the optic rod was only visible to the sighting eye when the gun is mounted. Therefore the cross dominant eye does not compete with the weaker eye, and the dot correctly floats with both eyes open.
Most do not realise this, but a T2 combat sight works the same way. Using a traditional scope, the majority of your sight picture comes from looking through the optic, hence the close eye relief to the eye piece. The tiny T2 does not work this way, and in fact, you do not need to see through the objective end at all, you only need to see the dot. This is why they are no longer shipped with see through objective covers, they are now solid black. The optic body is very tiny, and is designed to be mounted as far forward as possible on the receiver. In doing so, it obstruct very little of your vision, with the majority of your target being seen, with both eyes open, from around the T2 body, not through the optic. Like the Swedish device, only the sighting eye sees the dot, and when your brain puts the image together, the dot correctly floats with both eyes open. Now when I have good constant light, I need to make a precision shot, and/ or I have time to adjust the dot brightness, then my objective cover stays open. But, when I'm clearing buildings, going from bright to low light, and am in close quarters, then with the solid black cover closed, the dot can be left at the same setting, and is clearly seen, with the brain putting it all together so the dot correctly floats with both eyes open. You can take impact damage to the objective end, dirt, debris, etc...but against the black, the dot shows up crisp and clear.
So with all that said, if your daughter is measured on the extreme end of cross eye dominance, then likely switching hands is the easier route. But, if the cross eye dominance is not extreme, and you are looking for dots:
- Choose a red dot having a body that is small enough so not to be too obstructive of the target view with both eyes open.
- Mount the red dot as far forward on the receiver rail to lessen any obstruction of the target view with both eyes open.
- Use the largest appropriate dot size, for the intended game, to make it easier to pick up the dot.
- Resist temptation to close the off eye, and only look through the optic. Keep both eyes wide open and look at the target. The dot will be there.
Good Luck
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