Do infants who die before the so-called age of responsibility go to heaven?

Is it not dangerous to base theology on one Bible verse alone? Sadly many today seem to do just this.

I shall go to him, but he shall not return to me.

2 Samuel 12.23.

Many teach that upon David learning of his infant child's death (which was a judgment from God for David's sin), that when he said "I shall go to him" that his dead child would be with him in heaven. But is this so? It is written "in Adam all die." 1 Corinthians 15.22 (my emphasis). 

On the doctrine of imputation, A.W. Pink writes thus;

"The doctrine of imputation is as bitterly hated as those of unconditional election and eternal punishment. Those who teach it are accused of representing God as dealing unjustly. What do the Scriptures say about it? As we have seen, Romans 5 declares that death has come upon all men because all sinned in Adam (v 12), that "through the offence of one many be dead" (15), that "the judgment was  by one to condemnation" (16), that "by one man's offence death reigned" (17), that "by the offence of one judgment came upon all men to condemnation" (18), that "by one man's disobedience many were made sinners" (19). "In Adam all die" (1 Cor 15.22). God deals with men on the principle of imputation. The sins of the fathers implicate the children (Exodus 20.5). The curse of Canaan fell on all his posterity (Gen 9.25). The Egyptians perished for Pharaoh's obduracy. Achan's whole family died for his crime (Joshua 7.24). All Israel suffered for David's sin (II Sam. 24.15-17). The leprosy visited upon Gehazi passed to all his seed forever (II Kings 5.27). The blood of all the prophets was exacted of the members of Christ's generation (Luke 11.50)."

Adam being the federal head of the entire human race, through his disobedience, sin entered the world, and because of his sin, death is the lot of  all his descendants. David said:

Behold, I was shapen in iniquity; and in sin did my mother conceive me.

Psalm 51.5 (my emphasis).

When David said "I shall go to him", he was merely saying that he would go to sheol (his grave), because that was the abode of the Old Testament righteous and unrighteous dead.

It is, no doubt a very emotive subject, but are babies born sinners or no?
I can well understand why some hate what is known as Calvinistic theology, but as ever, "what saith the Scripture?"