Make sure she gets to try holding it and mounting it to her shoulder before you buy. Most youth shotguns are sized for large 14 year olds. My whole family is on the small side. When my boy was 12, it was not really practical for him to hold a youth-specific model 20 gauge, much less shoot it. I probably could have found him a smaller .410 but it's better to wait until they can fit a gun with a bigger pattern that will give them a better chance at success on birds.
Semi-autos have less recoil and that helps kids a lot if it fits them. For 4H shotgun, kids have done real well with 1100's and 11/87's. Nowadays I'd look at the Remington V3. But it must fit. Those 4H kids are usually 14 or older, and kids are huge these days -- a lot of them are bigger than I am by the time they're 14. The length of pull is the fitment that is most likely to be far off. You can cut the stock down and refit the recoil pad -- just don't buy something you're not willing to chop-to-fit. Semi-automatics and pump-action guns are longer in the receiver than singles and doubles. If they have a long barrel or a long magazine tube, those things add weight to the front end. That can help steady the swing and dampen recoil when the gun fits, but if the gun is over-size, that front-end weight just makes it even worse.
I bought a handy little single-shot because it was lightweight overall, had a shorter receiver than any repeater, and it had less weight and cost than a double-barrel. I was able to buy a second buttstock so I could have a full-length stock and one that is cut down to fit kids. One problem with a lightweight single shot is the felt recoil. I like 28 gauge for kids because it patterns better than .410 and recoils less than 20. But with 28 gauge, it's too hard to find ammo and not practical to get cheap target ammo unless you reload it yourself. There's also just a lot fewer choices in guns. So I got a 20 gauge. With 20 gauge, you can try to buy or load light target loads, but it will still be a lot more recoil than kids who've only shot a rimfire rifle are used to.
The best way to get kids accustomed to recoil without developing a bad flinch might be to gradually introduce recoil by handloading. If you don't handload for shotshell, you can handload for centerfire rifle. You could use a pistol-cartridge carbine, or make up some light loads of .223 with Trailboss. Graduate from that to full-power .223 and on up. But sending a small kid from a .22 rimfire straight to a 20 gauge that doesn't even fit them right is a recipe for a bad experience.
