If the dying child is a girl, then the answer is no. A woman's brain isn't fully developed until she is married so having sex with her is like bestiality, even if it's with another kid, and bestiality, much like eating eggs and dairy, is wrong.
If the dying child is a boy, then the answer is to get him an adult prostitute. He deserves to be liberated from inceldom before he dies. In fact it's critical, as otherwise he'll end up in the inferno, languishing in eternal separation from God (who's a woman btw).
Ethics is so easy. It's all so obvious.