I would say that if there is any chance your child might grow up and want to become catholic, baptize as a baby. I am a protestant (a lovely amalgamation of every German fringe church out there, if I want to get specific) but my dad was a minister, so I learned a lot about different religions and sects of Christianity. For a lot of Catholics, a lot of the pressure to baptize Catholic is a hold-over from the days when unbaptized children went to Limbo for awhile - even though that was abolished with Vatican 2 (I think), there is still the residual that this is what should happen. Also, the Catholic Church is fairly picky about who counts as Catholic (though that's also eased up some). But if your child is baptized Catholic, it's a lot easier for him or her to do First Communion and become a full-fledged member of the Catholic Church later on.
As for your confusion regarding baptism, here's the simple answer, as already explained by many other posters. Basically, Baptism is just a ceremony that officially welcomes the child into "the body of Christ" (i.e. - the church) and asks certain questions of both the parents and the congregation, all centered around everyone in attendance helping to raise the child as a faithful child of God. In Protestant and Catholic churches, for the most part, the child then gets to decide as they get older whether they want to acknowledge that promise made by their parents when they were children - Protestant churches call it confirmation and Catholics first communion. A lot of churches will not allow someone to take communion unless they are first baptized, which is another consideration.
However, if you feel very strongly about adult baptism, then I agree with the other posters that a dedication service might be a good compromise. The United Church of Christ has a baby dedication certificate, so they might also do the service. You might want to call a local church and ask. Hope this helped.