The path has some steep edges/cliffs that I'd be scared having my energetic 4 year old near.
If I did it id make sure I held hands with the 4 year old and had them walk on the inside of the path.
I did this hike before with a 3 year old, but I carried him all the way up and down the mtn. It's a longer hike than I guessed and my body was tired from carrying 30 lbs the whole way.