Can't say I would have a 6 year old shoot a handgun just yet, but you know your kid best.
I'm taking my 7 year old out shooting for the first time this summer and will have her shoot my 1955 Remington Scoremaster .22 bolt gun.
I will also let her shoot my 10/22.
I have a Ruger Mark I target model that I may let her shoot off a sand bag later in the year if she does ok with the rifles.
I also have a Ruger SR22 that is a blast to shoot (much better than a P22).
I'm not sure I can trust a 7 year old free standing with a handgun, but I'll see how she does with the others first.
Kids tend to forget the safety rules pretty fast when things get exciting and fun.
If you must... Ruger Mark 1,2,3 or other target style pistol would probably be best.