I have a 10/22 and love it, but I don't think a semi-auto is the way to go for a beginner. Sure you can make it a single shot if you load it one round at a time, but the 10/22 surely won't be as easy to load through the receiver as a bolt action would be. I myself have never found it easy to load the 10/22 one round at a time through the receiver. I guess you could drop out the magazine and load only one in that way, but again I think that is a lot of unnecessary extra work to load the gun when it could be done way simpler with a bolt-action. Also easier to see whether the gun is unloaded or not with a bolt-action. The 10/22's don't hold the bolt open after the last shot which could easily get a youngster confused whether the gun is actually loaded or not.

The 10/22 Ruger is one of the best Rifles out there for the money around $250 New, but if you want to save a few bucks for a beginner look into this Mossberg 702, shoots as smooth as the Ruger and about $150 New.

Teach her to shoot with iron sights first. A scope, if she needs one, can be added later.
Pete