I just picked up a Ruger LCR .22 and put 50 rounds through it today. The only problem I had was some tight extractions that eased up when I used different ammo.
While it is a decent gun, it is not what I'm looking for. I wanted a backup piece to my Ruger 10-22 rifle that I could use for hunting small prey. I would buy a Ruger SR-22, but it is off-roster in California. Because of problems I had with my other .22 semi-auto pistols (they only like CCI mini-mags), I decided I wanted a revolver. I may pick up a Mark III and try to restore confidence in SAs.
With the LCR 22, I was able to hit the black circle of my targets at 7 and 13 yards, but my shot groups were pretty bad. This is not surprising with a snub nose, fixed notch rear sight, and a hefty trigger pull. At 25 yards, I missed the black circle completely, but I probably wouldn't have missed a torso. In order to hunt small game, I think I will need at least a 4" barrel.
As I said, the trigger pull on the LCR 22 was very hefty, probably too much for a child, although the weight of the gun was nice and recoil was negligible. It will fit small hands well. On my S&W revolvers, I slicked up the action and put Wolff springs in. I'm not sure if Wolff has springs for Rugers.
I will probably sell the LCR 22. If you are interested and in California, I can give you a good deal on a barely used and already inexpensive revolver.
I will probably get either a Ruger SP-101 in .22, a S&W 317, a S&W 63, or a S&W 617.
The Smiths are around $800-900 new! If that's not too much money for you, then look at the S&W 63 or the 43C. I have a an old J-frame .357, and they are nice especially after a trigger job. Also consider the SP-101 which is substantially cheaper and a nice piece.
I am not particularly fond of the quality of my Rossi/Taurus in 44 magnum, so I would hesitate to buy their convertible 22LR/winchester magnum. Stick to Ruger or Smith, the latter being better quality at a higher price.
The Ruger Mark III is a phenomenal pistol that I think you should consider for your child. Revolvers are challenging weapons to fire well although they are easy to operate.