None of us can claim to understand God. He is incomprehensible. Yet He is also perfect love and perfect justice. The mortal condition of this child is not her destiny. Perfect justice is not something that can or will occur in this life. It simply isn't possible without overriding free will and that defeats the purpose of our mortality, which is to prove that we can be obedient and faithful to God.
It so happens that my faith believes we didn't just poof into existence at birth. I believe we existed in heaven before birth, as children of our Father in Heaven, and that in many cases we had a large part in determining the circumstances of our mortal lives--not in the sense of Karma or reincarnation or anything, but in the sense of volunteering to fulfill a mission along with gaining our mortal bodies. Thus, some of us live a long time, some only a moment, some in luxury, some in destitution. Each of us is only expected to "fulfill the measure of our creation" (which is different for each person) and return to our Father. Some, I believe, were so faithful and valiant in Heaven that they need only come to earth to gain a body and then they can depart back home to Heaven. And even some of those choose to stay here longer to help the rest of us learn compassion and empathy. In other words, the valiant souls are serving us and helping us to be more Christ-like. On the other hand, if we neglect these souls, we are accountable to God eventually unless we first repent.
Because I see this mortal life as a continuum or the second act in a three-act play, so to speak, I don't put that much stock in the second act alone. Just as a play doesn't stand by its second act alone either, neither does God's love and justice stand or fall by the second act alone.
Don't let the unfair things of this world keep you from feeling the Lord's love in your life. I get discouraged at the evil and unfairness in life also but I can also remember that as Isaiah says, our ways are not the Lord's ways, and our thoughts are not the Lord's thoughts. We can't hope to understand the Lord's ways because our understanding is so childlike compared to his. When I took my children to the doctor for their immunizations, it was difficult for me to let the doctor hurt them without being able to communicate adequately why they were being hurt. I could only hope my babies still believed I loved them more than anything and there must be some reason why Mommy let the doctor stick needles in them. I think the same thing applies to some extent to us and the Lord's ways. We are not capable of seeing the long-term visions of the Lord and knowing His purposes. That understanding brings me peace. I hope it can help you in your journey.
Your's was a very kindly post, and I appreciate your kindness and loving heart. I would not dream of attempting to argue against your faith. All I can say is I don't have the faith you do.