I've got an air rifle I want to sell...
...but I'm assuming you want something for her to learn bolt operation, etc. on instead of just shooting basics/backyard plinking?
Only .22s I have experience with are 10/22s and Marlin 60..the latter may be a bit big but is darn accurate. The former has a LOT of cycling issues, but size wise might be the right fit (I had 5 year olds using it last time I went). Both are autoloaders though, unfortunately, and it seems that is not what you're looking for. Good luck