Thanks for posting. If I understand this correctly, your church believes the Holy Spirit does indwell babies at baptism as it is a sacrament and as such confers Grace. If I am correct, it is a fundamental difference we have and thus we do have different core beliefs and as such teach different Gospels.
Is it fair to say I am relying on Scripture and you are relying on your church having it right? If I'm wrong where in Scripture do we see unbelieving babies indwelt by the Holy Spirit?
It seems so yes. And not just "my" church but also the Eastern Orthodox churches, the Oriental Churches, Anglicans/Episcopalians, Lutherans, and I believe Methodists as well. So if you're keen on holding that view, then you must hold all of those Christians teach a different Gospel as well.
Is it fair to say I am relying on Scripture and you are relying on your church having it right? If I'm wrong where in Scripture do we see unbelieving babies indwelt by the Holy Spirit?
No. Not fair to say. In the Catholic mind, Scripture and what the Church teaches can never ever disagree, because God who gave us the Scriptures also gave us a Church to properly interpret them. I would say, rather, that you are relying on specifically your interpretation or your church's interpretation of Scripture, and I am relying on my Church's.
Which gets to your second point. The Christian revelation cannot be artificially confined to merely what is directly stated in Scripture. If that were the case, we could never use the word "Trinity" or the phrase "Two natures in one person." Even though there are no explicit infant Baptisms in Scripture, they aren't explicitly forbidden either. So at most we can say Scripture is neutral.