That's news to me for a Calvinist to say children have eternal life.
Sure. It's four hundred year old news, but I guess it's news to those who haven't looked.
Since we must make judgments about God's will from his Word, which testifies that the children of believers are holy, not by nature but by virtue of the gracious covenant in which they together with their parents are included, godly parents ought not to doubt the election and salvation of their children whom God calls out of this life in infancy. Canons of Dordt, Heading 1, Article 17
This is addressed in the Synod of Dordt. Some children indeed do have eternal life.
I thought you believe in original sin. You guys quote psalm 51:5 Surely I was sinful at birth,
Sinful from the time my mother conceived me.
All have sinned, non are righteous. What happened to these verses?
Nothing. Nothing in the case of us sinners, either. Both have original sin. Both are subjects of God's mercy and thus His calling and regeneration. Both may believe.
Election "
does not involve his choosing certain human qualities or actions from among all those possible as a condition of salvation, but rather involves his adopting certain particular persons from among the common mass of sinners as his own possession. As Scripture says, When the children were not yet born, and had done nothing either good or bad..., she (Rebecca) was told, "The older will serve the younger." As it is written, "Jacob I loved, but Esau I hated" (Rom. 9:11-13). Also, All who were appointed for eternal life believed (Acts 13:48)." Synod of Dort, Heading 1, Article 10
Maybe I just don't understand Calvinism. If babies have eternal life or if they die before a certain time we know they are one of the elect? Would you say they were assured of eternal life until they do something?

No. They are
concluded to be elect because of the evidence God gives, "elect for the sake of their fathers." That's the sole evidence to go on: God's promises about election. If they reveal in maturity that they are not believers, then their rebellion shows they have not been reconciled with God. That is also evidence to go on.
Assurance arrives through a rather different path. We receive assurance from the Spirit of God that we are His, yes, and we also receive assurance from our works, and from our hearts. The assurance from God the Spirit is infallible -- yet we may be deceived by others who tell us, one way or another.