In addition to nickpsecurity's response - if you enjoy using the rationalist perspective, then the calculus is that yes, the innocent child died a horrible death, but then they spend eternity in heaven.

I don't subscribe to "it's worth torturing one person for their entire life if it removes dust specks from enough peoples' eyes" hyper-rationalist logic, but I do think that "an eternity of peace and joy outweighs a few days of suffering" is a reasonable argument to make. (and the more you think about the length of infinity, the more reasonable that argument gets)

Also, my understanding of the answer to "why do innocent people suffer" starts out with the caveat "Nobody is truly innocent - everyone sins a lot (the standards of a perfect God are zero sin, not "not very much sin")" and then under that caveat there's a few reasons:

1. God's punishment/wrath on non-Christians

2. God's correction on Christians for sin (like punishing a child for disobeying something important like "don't hit others" so that they don't do that when they grow up)

3. God pushing non-Christians into a state where they'll realize they need Him (I've heard a lot of stories that basically go "my life started out OK and then I did alcohol and drugs and eventually ended up in a ditch and realized I needed Jesus")

4. The result of other humans being created with free will exercising their free will

5. God bringing Christians closer to Him (to your last point)

6. God using that person's suffering to either bring other Christians closer to Him, or to convert non-Christians

...where the reason for any particular case is probably a linear combination of the above.

For the specific case of the person dying instead of just suffering, take (1), (4), (6), and "it was in God's plan that it was time for this person to die" (e.g. because they were a Christian who He was ready to take to heaven, they were a non-Christian who He knew would never become a Christian, they were going to do something evil in the future, etc.)

A lot of the reason why people think so many things in Christianity are crazy is because their perspectives are wildly different. For instance, in almost every non-religious people have some threshold value for what it means to be "good" that still includes occasionally doing something "bad". But where does that value (and "good" and "bad" for that matter) come from? The Christian answer is that "good" things are things that are not sin, "bad" things are things against God's will, and that the threshold value is "perfect" because God is perfect - which seems nuts, but I think that it logically follows from the premises, and if you understand all the premises at once, the entire thing seems quite logical to me at least (although most people don't actually believe the premises without a major ego shift).

You do have to understand the premises, though - if someone says "they weren't baptized" I can guarantee you that their theology is inconsistent and they don't understand the premises. There's a reason that Martin Luther nailed his 95 theses to the door of the Catholic church - not only was the church incredibly corrupt, but the theology itself is inconsistent with the Bible.

Uh, I hope this was helpful. I don't expect you to believe it, but I at least hope it's logical. If all that was rational to you, then you can challenge me with more hard questions at the email in my HN profile and we can see how far I can get before I run out of answers :P