If you are lucky, there will be a club doing CMP Rimfire Sporter nearby.
http://www.odcmp.com/NM/Rimfire.htm
It is less equipment intensive than regular NRA Smallbore. That 10-22 would get her started and could be upgraded or replaced with something like a CZ455 when she got really interested. The club here shoots it and has a good time and a few have moved up to the harder and more expensive Smallbore.