A couple months ago I began to look into a baby dedication ceremony for Evelyn. I emailed the church that Kevin and I sometimes attend and found out that they don't do it (most likely because it's a huge church and they don't have time). So I recently started doing some research for myself.
I realized that there isn't actually much of a biblical basis for what we know as the baby dedication ceremony. Every example I found in the Bible had no clergy involved. Parents might dedicate their baby to God's service once they found out they were expecting (I Samuel 1:11), but there was no ceremony after the baby's birth. Examples seem to show the parents alone committing their child, and doing it before birth (there are a few examples in Luke 1).
And it seems that there is no actual ceremony in the Bible. Examples I found seem to be moments of spontaneity, not a planned event. When Simeon took the baby Jesus in his arms and blessed him, Mary and Joseph were taken aback; they were not expecting it. Plus, that was a one-time thing because Simeon recognized the Messiah; this wasn't something he did to every child he came in contact with. One might take the example in Matthew 19 where Jesus says to "let the children come to Me" as a reason for baby dedication. But if that were the case, He might have also said "And let the babies be brought as well." Plus, the parents watching weren't looking for any kind of ceremony. They simply and spontaneously took advantage of Jesus passing by and asked him to bless their children.
Finally, in researching, it seems to me that the baby dedication ceremony runs parallel to infant baptism. Perhaps it took the place, once some people began to realize that infant baptism isn't biblical but still wanted some sort of public ceremony.
So if a baby can actually be dedicated to the Lord at birth, what does that look like? It seems to me that the occasion arises as soon as the parents realize the baby is on its way. And they are the ones to do it, though others may rejoice with them in it (like Simeon or Anna or Elizabeth's neighbors). The parents are doing it from that moment onwards, hardly letting a day pass in which they don't dedicate or commit their child to the Lord.
So it seems to me that after learning all of this, I can no longer pursue an infant dedication ceremony for my daughter. Perhaps in the hospital on the day she's born, there will be an impromptu moment of family gathering and praying for her (and plenty of rejoicing, to be sure!). And although it seems to go against what is ingrained in us as Christians, there will not be a public ceremony in a church. So that's that!