The proper sequence of events (believing / salvation and THEN baptism) is clear in Acts 8:34-39:
34 And the eunuch answered Philip, and said, I pray thee, of whom speaketh the prophet this? of himself, or of some other man?
35 Then Philip opened his mouth, and began at the same scripture, and preached unto him Jesus.
36 And as they went on their way, they came unto a certain water: and the eunuch said, See, here is water; what doth hinder me to be baptized?
37 And Philip said, If thou believest with all thine heart, thou mayest. And he answered and said, I believe that Jesus Christ is the Son of God.
38 And he commanded the chariot to stand still: and they went down both into the water, both Philip and the eunuch; and he baptized him.
39 And when they were come up out of the water, the Spirit of the Lord caught away Philip, that the eunuch saw him no more: and he went on his way rejoicing.
And Philip said, If thou believest with all thine heart, thou mayest.
It must be kinda hard for little babies to believe in their hearts; but I guess it must be true.