I was raised as a Presbyterian, although I am no longer an adherent of a particular religion. The Presbyterian Church encourages infant baptism, but interestingly, a lot of the rank and file don't baptize their children as infants.
I was baptized when I "joined the church" at 13. Joining the church (some churches now call it confirmation, as do other Protestant denominations) involves taking a class on the doctrines of the faith, meeting with members of "The Session ( the elected officers of the church), and declaring one's faith. At that point, you become a voting member of the church. It's a democratic organization, so there are no bishops etc. Rather, there is a hierarchy of governing bodies made up of elected representatives (the presbytery, the synod, the General Assembly) which make decisions about church policy.
You could conceivably ask your daughter to wait until she is old enough to take the class, so that she really understands what she is getting herself into.