The 10/22 is a good & modest priced option in a .22 rifle. I'd also get her a brick of ammo for it. That's gonna cost ya today.
A question to ask yourself is "Where is she gonna find ammo and how much will it cost her ?" I don't know about your area of the state, but its extremely rare when I find .22LR ammo in a local store. You pretty much have to luck out and walk through the door right at the time they unload it, because it'll be gone in minutes. (This happened when I walked in a store yesterday, missing the .22LR they had during the 10 minutes it remained on the shelves.) And most gun, sporting, and big box stores in our area never get it in. I'd imagine this would be frustrating for a new shooter with a new rifle.
Of course, if cost isn't something needed to be considered - and paying $60 or more for a brick off the web is o.k. - maybe none of this matters in this case.
Something to consider after she's had her .22 and shot it for awhile is an air rifle. No, its not the same as a powder burner. But, at least you can find projectiles for them and its not outrageously expensive to shoot. I had BB guns as a kid, but stopped shooting them after getting my own .22 rifle at around 11 years old. I've taken up air rifles recently because of the ammo shortage situation and the convenience of being able to shoot in my own back yard. I regularly shoot various targets out past 100 yards with the air rifle. (Its a big back yard.) The main limitation with the air rifle is we often get heavy winds. But that would be a factor with a .22LR rifle also.
Range bags are nice to have. Not really needed for a .22 rifle though. If she had eye/ear protection, she's good to go. The ammo can fit in a jacket pocket.