Unless you are really determined that it just has to be a forteener, Mt Agassiz (just under 14), from Bishop Pass is doable as a day-hike from the South Lake trailhead in less than 12 hours. Plenty of good camp sites along the approach trail, if you don't want to do it as a day hike. The West Slope route is class 2, with solid rock, no exposure, and easy route finding. It would be a good climb and safer for your kid than some of the other climbs.
http://www.summitpost.org/mount-agassiz/150921The view, from the summit of Agassiz, of the Palisade glacier and beyond is outstanding.
