You've received good advice here. I would only add a couple of things (and I may have missed them in other's comments).
1. A .410 single shot has long been a child's first shotgun. I still have the one I got as a youngster, and it kicks more than the Mossberg 500 bantam 20 gauge that I have for my wife and kids. It's lightweight, and just plain kicks. Be aware of things like this.
2. Even with low brass loads, that Mossberg 500 20 ga kicks more than my 7 year old daughter (tall, strong, athletic frame) would appreciate. She hasn't been allowed to pull the trigger on it for that reason.
That being said, my oldest daughter (the 7 year old) is DYING to get to kill her own turkey this year! She's been shooting a 22LR for a couple of years (great advice from BOWGUY...start here), has shot a .223 AR several times, and is a consistent shooter. IF I decide to let her get behind the trigger for a turkey of her own this year, it will either be with a crossbow, or after having proven that she can handle a light bird load from the 20 ga.
Also, IF we go the shotgun route, it will only be AFTER I add weight to the stock, and add something like a Limbsaver recoil pad.
When she hunts with me, she wears Walker electronic earmuffs at all times, unless we are walking. They are around her neck and ready to be put on even then, though. I recommend something like that. Cutting down on sound absolutely makes a difference in perceived recoil.
