We do the same sort of thing--babies are "dedicated" which is what we call our blessing, it's a prayer and annointing of the child, and a prayer for the parents, too, that the child will be raised in a Christian home, and eventually make a public profession of his or her faith in Jesus as Lord and Savior, and will be baptized following that profession. It's very different from Christening or Baptism of an infant. At my church, our pastor does the blessing, assisted by one of the deacons, in other churches, just the pastor does it...it can vary, but the pastor is always the one who does it, sometimes assisted by an elder or deacon, sometimes not, sometimes assisted by other clergy on staff, sometimes not.
My pastor always makes it clear in his little talk about what a baby dedication is that it is very different from Christening or baptism, and that a blessing in no way imparts any kind of salvific power on the baby. People do get confused and wonder why we as Baptists bless and dedicate babies, but then require people to be baptized all over again as adults--then we have to go into this long explanation that the baby was never baptized, so no one was being rebaptized. Ah, it's so confusing LOL.