Old School is right. This is the tradition PB belief. And the traditional "Calvinistic" belief."We do not believe all the elect will hear the Gospel."
We know that we are saved by grace through faith in our Lord Jesus Christ (Eph 2:8-10). We also know that is no other means of salvation except through Christ(Acts 4:12). Within the Baptist ranks, both free will and sovereign grace sides should agree on this. (can't speak for other denoms)
One can not biblically say that infants that die are saved if they have excluded election.
Yes, the bible said David said "this". But it was said about his child and not children in general.
There is also room for debate that the statement itself was a historic account rather that prophetic or inspired statement such as the Psalms of David are.
There are a lot of "hints" throughout the bible such as David's statement or Jesus' love for children or Jesus referencing the saints as children or little ones.
Another hint is Abraham questioning God asking, "That be far from thee to do after this manner, to slay the righteous with the wicked: and that the righteous should be as the wicked, that be far from thee: Shall not the Judge of all the earth do right?"
But, again, there is nothing in the bible that outright states that infants that die are saved.
But What about Election. God's Will, God's Decree, God's Sovereignty.
Those that uphold the doctrines of Grace, We can firmly state that ALL God's Elect will be saved regardless of any situation.
I personally can say with Christian liberty, that I believe young children that die are elect therefore saved. I can say that as a personal belief because of the hints AND most importantly, I know that all God's elect will be saved.
Steve