Wonderful story. My prayers are with them.
As an aside, my brother's a surgeon, and he says kidney transplant is truly one of "the best most satisfying surgeries.". He says there's nothing like that moment when the kidney "pinks up" and a very sick person can become quite well very quickly.
It sounds like the little girl's case is more complicated, but I will hope for the best.
Incidentally, on the other side of the spectrum from the kidney is the liver, says Brother Lugz. Whatever you do, don't F up your liver.