i think the 10/22 would be a great choice for a starter gun. Some people are getting wrapped up in the fact that it is a semi-auto. I'm sure when she is learning she is going to be supervised, so just give her one round at a time. Presto-chango! now the 10/22 is a single shot!
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.