I started flying when I was 12. I flew all throughout my teens, soloed at 16 and got the private certificate at 17. I was so fortunate to have parents like yourself who saw something I loved and decided to let me chase that dream. 22 years later I'm at my dream job flying at a US major airline. I'm constantly thankful that my parents allowed me to fly at that age!
As far as using flight simulators... Go for it. I was always on my PC back then using flight simulator. I'd make flight plans, figure out approach charts, and even taught myself how to use VOR's and NDB's. It's all good and will keep your kid engaged when not flying the real thing.
Also, one huge piece of advice. This is easier said than done. Get an instructor that'll last. You don't want to constantly be changing instructors over the years if you can help it. Someone who can also be a mentor will help immensely when your kid gets a little distracted with other teenage stuff (trust me, it'll happen).
I'm still in contact with my old instructor to this day, and credit him with really shaping my perceptions of what I wanted to do with this career.
Good luck, and feel free to send me a PM any time.