From John passage on this in his First Epistle, I would say you are right. This was at a later date.
6) This is He that came by water and blood, even Jesus Christ; not by water only, but water and blood. And it is the Spirit that beareth witness, because the Spirit is Truth.
7) For there are Three that bear record in heaven, the Father, the Word, and the Holy Ghost; and these Three are One.
8) And there are three that bear witness in earth the Spirit, and the water, and the blood: and these three agree in one.
9) If we receive the witness of men, the witness of God is greater, for this is the witness of God which He hath testified of His Son.
10) He that believeth on the Son of God hath the witness in himself: he that believeth not God hath made Him a liar; because he believeth not the record that God gave of Himself.
I John 5:6-10
As you have noted the Apostle John gives no eyewitness account of the Baptism of Jesus in his Gospel. Yet he refers to John the Baptist in John 1:29-34 as giving record to Jesus as the Son of God, but John the Baptist stated he bare record that God bare record that Jesus was His Son, remember John stated:33) And I knew Him not: but He that sent me to baptize with water, the Same said unto me, Upon Whom thou shalt see the Spirit descending, and remaining on Him, the Same is He which baptizeth with the Holy Ghost. 34) And I saw, and bare record that this is the Son of God. John 1:33-34 strong text The Baptist mention water so that we might know that Jesus water baptism, was God record to the World that our LORD Jesus Christ and the Holy Spirit along with the Father are Three separate Person, yea United as One Godhead/Trinity. Yes I say God's record because all Three Members of the Godhead; the Father, and the Word (Who of course is the Son), and the Holy Spirit gave a heavenly witness because the Son was sent from heaven, the Holy Ghost descended from heaven as a Dove, and the Father's voice, came down from heaven.
While we continue to read I John 5 after verse 7, which many modern scholars question; we see the Apostle John state if we receive men's witness the witness of God is greater. Yet even Jesus tells us that many will not receive His witness--John 3:11; 32. So that we see that the record of the Trinity came at Jesus Water Baptism, hence Jesus came by water. We know that Cyprian in 250 AD, quoted the TR complete verse of I John 5:7 with the only difference being instead of the Word, he called Jesus the Son.
But what was the witness of men. We see in I John 5:6 that Jesus came by water but also water and blood. In John 19:30-37 we see the Apostle John bearing the witness of men. For in at the end of verse 30 John states that Jesus gave up the Ghost (Spirit). But we also see at our Savior physical death, that instead of breaking any bones in His body, they pierced Him with a spear and what came out, blood and water, John 19:32-34. So that the Apostle states that he bear record in verse 35, So that at Jesus death we see that the Spirit departed, which is a sign of death, and blood and water coming out of the side agree with this sign.
So I see John in his Gospel, in passing mentioning Jesus baptism, after it happen, but later in his first epistle, mentioning it again in I John 5:7 as the Heavenly Witness; for all Three Members of the Trinity were presence and this according to John the Baptist was the Father record. While at Jesus death we see John baring witness, to the Spirit departing and the blood and water coming out of His side.