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Calvinists rightly teach that persons dying in infancy are saved in the same manner as are saved adults. God has only one plan of salvation. It teaches that sinners are saved by God's free and sovereign grace in Jesus Christ, totally apart from any works of righteousness they perform or any supposed virtue in them. Everyone who is saved — including all persons dying in infancy — is saved through being elected to salvation by God the Father, redeemed by the blood of Jesus Christ, and regenerated or born again by the Holy Spirit (as set forth in preceding messages).

I think I can fully agree with that statement. I believe that it is God's sovereign will that infants are saved even without any exercise of faith and that adults are saved through the exercise of faith. In all cases God's election is predicated on God's terms.

Yes, and in all cases, Regeneration precedes Faith; for Faith is God-pleasing, and the Bible adamantly teaches that while a Human is yet Unregenerate, he NEVER, EVER chooses to perform anything that is God-pleasing in any circumstance whatsoever.