I can't confirm this because I haven't tried it personally, but I'm pretty sure that my Savage MKII bolt action chambered in 22 LR would shoot shorts just fine and most likely feed them properly out of the standard magazine too. Other people who have tried it report that eventually fouling after shooting a great number of 22 shorts will make it hard to chamber and extract 22 LR ammo, but regular cleaning will solve that problem.
My friends and I had a number of different 22s as a kid and we shot all sizes of ammo from them without concern. Of course that was way back just after the invention of gunpowder, but I can still remember that no sparrow was safe in my neck of the woods.
Depending on the size/age of your daughter,maybe another option would be to look for a new Cricket. You just might even find a used one. There are several different extremely small rifles designed like this nowadays. They are single load,single shot,pull back the plunger type,and are extremely safe. I would think these,along with some 22 CB caps or some of the "no gunpowder" loads,would be a great training tool. --- SAWMAN