How old is your girl, and how big is she for her age?
Then decide if she is going to be able to repeatedly #### a break barrel air gun, keeping in mind that we are NOT discussing a Magnum-class, adult-size springer here.
Take a look at the Slavia 631 and if you are not too prone to getting all cheap, the smaller Diana models.
Here's the breakdown as I saw it as a kid. A spring gun was the best choice. #### it once per shot, only cost to operate was ammo, few seals to go wrong. They recoiled a bit. Almost like a firearm!

A pneumatic gun was almost as good, with it being more work, but still, the only cost out of pocket, being pellets. You end up tired of pumping up yer Crosman 760 in a hurry though. Four pumps is good for plinking. No recoil.
CO2 was dead last,lots of fun while the money lasted, easy, no work at all, but every shot cost twice as much, and about half the shot were unreliable because of the way CO2 eventually runs out...Not so good.
Take a good look at the Diana or Wierauch (spelling?) spring guns in the 'kid' sizes. They are not so powerful as to cause a lot of issues with strength requirements. Cheap to shoot, and well made.
Take a good look at the single stroke pneumatic Daisy target guns. The Cadets use them in their marksmanship program, and depending on exactly which version you buy, you can get adjustable stock lengths and pretty good accuracy with pretty much zero recoil. The technique for compressing the air is easily learned.
D&L Airguns have these and others on their site.
Cheers
Trev