Several things come to mind. You have to consider the motivation of the child, how much physical activity has the child done, and especially how much hiking, climbing, trail walking etc has the child done.
When we lived at almost 7,500' in 1971 our family did alot of hiking with minor elevations up to maybe 10,000'. My youngest, daughter aged 5, climbed Pikes Peak with my wife, son, age 8 and myself. This involved a 7 mile backpack to 10,000' + and the next day 6 more miles to the summit, 14,110' and then 13 miles back to the car at the trailhead. True this was not a 1 day hike as the overnight broke up the trip, but still quite an accomplishment in my opinion for a 5 year old. especially the last day with 19 miles.
Chris you were given good advice in my opinion as your two were a little young probably for that high an altitude, but others may have a different opinion, ie the Drs on this site.
