We have a number of small guns in our rack, and our granddaughter has always had the pick of them for shooting.
Here's a general summary of her reactions:
Most have barrels too long for ease of holding and aiming for small folks. They might be "light" to us, but to short folks that longer barrel becomes an issue.
Most small cals have a lot of steel out front due to heavy barrel walls on blanks too heavy for small cals. Read above.
Our granddaughter's pick of the litter is a short little
Pedersoli Frontier Carbine in 50 caliber. It's short and very light out front due to thin barrel walls, and very easy for her to hold and aim.
With 30 grain charges it recoils no more than your average small caliber, and that little powder charge is easy on the ears.
When the day comes and she decides to poke a deer, she'll already have the right gun in her hands. Meanwhile the targets and snowshoe hare catch heck.
Yeah, they're expensive when new. But keep your eyes open for used. I only paid $300 for mine.
Edit:
Can't seem to find it among their current models, even if the standard Frontier is still there. Their
Dixie Cub looks to be similar and tips the scale in the same 6# range as my Frontier Carbine, if you want to look at that for spec comparisons.