I was 29 years old, had two years of lessons while I was finishing my masters degree (not music related), then lessons stopped for ten years and now since a few months started lessons again. I am basically just beyond the beginners level.
I do have young kids, they started to hit keys when they were able to pull themselves up on the piano. I always took them on my lap as soon as they could sit with support and start playing simple songs with one hand or even finger and sing with it. My oldest was able to hum a melody when he was around one year. And then I mean recognizable. He is now a singer in several choirs, including the honor chorus of his school district.
Number two is following his footsteps en will join a children's choir this fall. He plays violin, has a nice voice and a good ear for pitch.
The third one has a strong voice, clear, on pitch. She is only five years old. She wanted me to start her on the piano, which I did. I took her in for five minutes with my son's and my teacher and she now sits nicely upright, holds her hands and fingers in a decent position (as far as I can see) and plays her way through book number one of the Alfred series for kids. No formal lesson, no pressure. She says she want to play the violin, but also cannot wait until she can join the kids church choir again (she was the youngest participant ever in that choir, but we held her back a little until she can sit/stand still a bit longer and probably will be able to read).
The youngest is humming along in pitch when we are singing or playing. he want to hit the keys when I am playing piano. We will see what he likes to do with music, or not.
So it definitely pays off to play a bit with your little one at the piano, just for fun. I do not start formal lessons until they can at least pay attention for twenty, thirty minutes and this can be different in each kid. In my experience as a parent and ex-schoolteacher, this is around six, seven or eight years old. The above is not an illustration of the musicality of my kids, but more an illustration of what may come almost on it's own in a relaxed way if you just pay a little attention to it, but are not forcing anything.
Supernanny