One of the most interesting aspects of Palm Sunday is the role children play in the event.

As Jesus makes his triumphal entry into the city of Jerusalem, children join in singing praises to Jesus. We just sang about that in our opening hymn, “All Glory, Laud, and Honor”: “all glory laud and honor to thee Redeemer king, to whom the lips of children made sweet hosannas ring.” We just imitated that event as our children processed with palm branches and sang a song of praise to Jesus. The cry of Palm Sunday is “hosanna,” meaning “save us Lord!” and the children make that cry.

Now, you may not think of Palm Sunday as an event that has anything to do with infant baptism. You may not think of this event as proof for infant baptism since baptism had not yet even been established as the sign of the new covenant. But this event is fully consistent with infant baptism because it shows us how God views the children of his people. Palm Sunday shows us that children of God's people are part of the congregation that praises him, they are part of the royal priesthood gathered in the temple to worship the Lord. 
What’s even more interesting is that the Lord Jesus not only receives the praise of children, he defends them against their detractors. This is a common theme  in the gospels: Jesus defending  the place of children in his kingdom. When the priests and scribes complained that the children were praising him, Jesus pointed out that their praise fulfilled the words of Psalm 8: “out of the mouths of babes and nursing infants he has ordained praise.” And so today, these children are brought for baptism in order that they too may become part God’s royal priesthood, the people who offer him worship in his temple, the children whose cries of praise fulfill Psalm 8. That’s is our expectation of what God will do here today.
It’s also important to understand that at whatever age someone is baptized, the same baptism is received. There is only one baptism, one kind of baptism, and so baptism always means the same thing. Baptism is God’s gift of love, uniting us to Christ and to his people. And, again, we have every confidence this will be true of these children being baptized today.