+1 on starting them with a Tenkara rod & line. Easy to cast - weights < 1.2 ounces total - short - easy to handle. I wish I had access to Tenkara when my boys were young.
As far as what age - it's not about age - it's about desire on the part of the child to learn. Let them set the pace and duration - and leave your rod at home when you go fishing / teaching.
Don't forget to teach about bugs and water and ecology - make it FUN and they'll want to come back with you.
I bought a microcope and brought it to the stream and we'd sample water - look a leaves, etc under the scope and before we knew it - a whole afternoon was gone and some of it was fishing - but it was all good times. My sons (now 22 and 25) still talk about doing "stream research".
Oh - and if they bring home a crayfish - don't forget it in the container....they tend to stink after a day or three.....