We overtook a mother cycling with her approximately 5 year old son. That is to say, she was dragging two bikes and the son over tree roots up a hill. The happiest noise of that party was the spokey-dokes clattering as the wheel turned on the boy's bike.
Now, you will think I am trying to put you off. Not at all. Just be aware of your child's abilities, and your own.
I have *walked* with children and there were days that pilgrims passed us and would be saying "be careful walking with kids, I saw this six-year-old having a hissy fit on the side of the path". It happens. Maybe that's what was happening for the cycling mother we saw. We offered assistance and when she declined, we overtook her and left her to deal with the child - if it has been me, I'd have been inclined to sit down together and have some food and move on when HE was ready to ride his bike.
We went back for more - it really is a wonderful experience and a couple of my boys who have walked are now saying hey would like to cycle it!