I don't know the answer to this, but the consensus here seems to be that they do go to heaven. I want to believe that but I have difficulty in making sense of it. The passages from scripture that claim one way or the other don't seem real proof to me when read in context.
Does that mean that babies who are born in environments where the gospel will never be preached or available are better off dead than ever grow up? Cause they won't be introduced to Christ when they do grow up so heaven won't be accessible then, but it is when they die as a baby?
It's really harsh to consider that babies would potentially go to hell, but outside of that there's the harsh established reality that we all deserve hell. We are sinful in nature due to Adam's original sin and Christ was sent to us as an immense grace from God, which we are to cherish with our whole being if we are to be saved. Salvation isn't owed to us at all, we don't deserve it whatsoever.
This means that your non-believing neighbour who's the kindest person you have ever met is also destined to hell, as well as people born into slave camps in North-Korrea who never heard the gospel. Why do babies deserve heaven then I wonder? Because they aren't accountable? People who never heard of the gospel seem to me just as unaccountable as babies when it comes to salvation. Why are babies special here? If you have never heard the gospel as adult you could never have made the choice to believe in Christ, yet you are still going to hell because salvation is not owed to anyone. I have then trouble processing how babies would get a pass nonetheless.
I truly don't know at the moment. And I fear the subject is too emotional for many people to have a genuine look on it. (Maybe it's sinful pride that makes the idea of babies going to hell unfathomable?)
Hello SamRF, first off, since I see that you are a new member,
WELCOME TO CF 
As for your OP questions, unbelievers will not be judged on the basis of something that they neither know nor understand, rather, they will be judged on the basis of what they ~do~ know and understand of the law, even if that is nothing more than the law that God writes on our hearts.
Romans 2
12 All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law.
13 For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous.
14 Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law,
15 since they show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts now accusing, now even defending them.
16 This will take place on the day when God will judge men’s secrets through Jesus Christ, as my gospel declares.
Unlike your kind, but sinful and unbelieving neighbor, unborn babies, infants, toddlers, etc., neither know, nor can they understand the law, even the law that God has written on their hearts, so there is no basis for His judgment and condemnation of them (also, the Bible tells us that we are judged on the basis of the sins that we've committed personally, not on the basis of our fallen nature).
God bless you!
--David
