That is my view as a non Calvinist. I guess to a Calvinist, it would not matter. The kid is either elect or non elect.
We do not know who the elect are just like you don't know who will receive the gospel and who will not. The only way you can know is preach the gospel to them and see how they respond. Until they are dead and buried they are the audience for gospel teaching and preaching. Election does not specify the names of who and who will not. Election does not specify the age when they will be saved. God has not only chosen his people "to salvation" but he has chosen the means "through" which he will save those people - preaching of the gospel.
With regard to children you should not force them to make a profession (many do through fear tactics and pressure) and you cannot determine the age they should believe. The Bible nowhere makes it a qualification to fill the office of Pastor or deacon that their children must be saved or be believers. I know one text is twisted to make that conclusion but that text simply uses the word "faithful" and then defines what that means - not unruly or riotous.
All my children made professions of faith during their early childhood (7-13) and I made it a point not to put pressure on them, scare them in any way but when they asked questions I answered them and of course prayed for them. However, after some reached adulthood and left home at least two recognized they made false professions. One of those two became a true believer with manifest fruits. The other one presently hates God and the bible and wants nothing to do with either. However, I never give up on that one child and as long as that child breaths I am going to pray for their salvation and share the gospel when that child allows me.