Did with my 7 y.o. son. Take care on the steep "stair" descent. Rock scramble along the shore is challenging. Beautiful, fun, and doable, but do not underestimate the difficulty. Give yourself at least 3 1/2 or 4 hours of daylight if you are hiking - esp. with a child! Saw a few dogs but they did not look too happy about it. Great trail maps and descriptions available at http://www.njpalisades.org.
Calogero Z. on White Shore Trail