Children are just little people. When it comes to fate or the hand of God, they don't get special consideration just because they are new to this world. I'm not trying to sound harsh, just realistic because we are all headed down the same road. So I see several possibilities, "shit happens" can be valid for all of them.
1) There is no reason, there is no plan. (Atheists like this one) BTW, if we exist for 1-100 years and then it's all over, what is the point, and why bother?
2) You are here to experience life, and for lack of a better reason, to improve yourself, with no guarantees of how long that experience will be. If you lean towards believing that your existence continues after physical death, then it's not that big of a deal, because your time on Earth is like experiencing a very short simulator ride. If you think you could have a spirit with an unknown existance-span, maybe eternity, then the time you spend on Earth, even if you live to be 100 is miniscule as compared to your real existence in the after life. The other possibility in this line of thought is that you make repeated trips to visit and experience this plane of existence. (In which case I see no reason why it has to be Earth. Could be some other populated planet anywhere in this huge universe we live in.)
3) In the traditional view, if God (as defined by Christians/Muslums) does truly exist, then he most likely is not proactive in this physical plane, otherwise (as I said before) why would so many bad things happen to good people? The only explanation would be that regardless of how bad you have it here, there is always an opportunity to better yourself and your reward, only if that reward is self improvement, is realized both in this life and at some other continuing level.