Corius,
I am from Nebraska, too (and there is one other new member that I know of from Nebraska as well). So... WELCOME! to the forum from the Cornhuskers (AKA Bug Eaters)!
If you are under any local or county ordinance zoning, you had better check into them before constructing a pond of 6 feet depth. They may require you to put a fence around it if you are within the zones of a village or city. In Fremont the max depth is 18". If you are out in the boonies, you can probably ignore this, but be aware just in case.
You might be over-doing it on the depth, but it makes sense to get that far into the ground to take advantage of the ground temperature and the insulating quality of the earth during cold winter / hot summer to level out the extremes. I might opt for 3 feet below grade and one foot above. That would be less construction and still plenty of depth with less exposed above grade. That is, unless you are planning on installing pond windows just above grade to see the fish from a seated position on your patio or the like.
As for the width and length dimensions, I agree with the previous responses that 6' x 6' may be too confining for Koi. That sounds a bit cramped for large, adult Koi to me and I am not a Koi keeper. I suppose it depends upon how many Koi you expect to keep in there. Two or three might be OK??? But you could keep many of other smaller varieties just fine.
My Mom lives in Fremont, NE and her neighboor has a small (5'x10') kidney shaped pond, 18" depth with 15 goldies or comets in it. All about 6" length. They kept all this winter just fine. He had to break the surface ice twice during the really cold snaps to allow the pond water to gas out, but he kept the recirc pump running all the time and so the pond never froze solid. That is key, keeping the water moving and free from harmful gases and plenty of O2.
As for child-proofing, the best options are simply supervision, education, discipline and respect. If you can't get those, an electric fencer works pretty darn well! Hee Hee (sorry, redneck humor there).
Catfishnut