Savage Rascal. It is, IMO, superior to the Cricket. Safety is easy to see and independent of the bolt, real accu-trigger, decent sights.
I would never waste my money on a Cricket again. Cheap POS gun. I don't know much about the savage...but the Cricket was only useful to my daughter for a short time. She is now 10, has outrown it. I bought it for her when she was 8. If you're stuck on a bolt action...maybe the Savage would be a better choice.
I have a 10/22 'carbine' I think they call it. Thing is featherweight. She handles it nicely. I should have just gone to it.
I do agree a bolt action is good to learn on, but I spent 175 on the cricket I bought(pink laminated stock, not cheap toy looking plastic you see everywhere). I should have just spent another 25-75 on a 10/22. I saw a pink laminated stock 10/22 I would love to get her this Christmas but she'll keep borrowing mine for now.
I wanted to move her to the lever action...but the dang henry was about twice as heavy as the 10/22!
Ruger does make a single shot mag for the 10-22.
What about the Ruger American Rimfire youth model? They have the interchangeable stocks to alter length of pull. Once they get bigger, you can put the full size stocks back on. One rifle from age 5 to adult.
I haven't looked into how short the length of pull is or the weight of the rifle. It might be better a few years from now for her.