When the Savior appeared to the Nephites in 3 Nephi: 11 he called Nephi up in front of the group and gave him the authority to baptize. Wasn’t Nephi the prophet at the time? Didn’t he already have the priesthood and authority to baptize?
The answer to your question is YES. He did have the authority to baptize prior to the Visitation of Christ to the Americas… under the Mosaic Covenant. But Christ, having fulfilled the Law now established a new order with a NEW Covenant.
Elder Jeffrey R. Holland explains:
“Although these Nephites had authority to baptize in the old Mosaic dispensation, Christ invited Nephi forward to affirm his priesthood authority to baptize in the new gospel dispensation, and perhaps to ordain him to the apostleship at the same time [see 3 Nephi 11:18–21; History of the Church, 4:538; D&C 20:38]. Then he called another group forward, instructing them how to baptize and noting that there would be ‘no disputations’ among them on this crucial doctrine”
— Christ and The New Covenant: The Messianic Message of the Book of Mormon  259–60.
Prior to this, part of the “disputations” that the Lord refers to was the fact that they figured “ordinances” of all kinds were done away. Such is the condition of most of Christianity today. Unlike the Jews of Jerusalem, the Nephites still maintained the knowledge that the Messiah would fulfill the Law of Moses. Some of them did not understand that baptism would be part of the everlasting gospel.
So to settle the dispute once and for all. He publicly gave Nephi and the others the power to baptize under the NEW covenant and dispensation. He also did this to publicly declare there was a new organization that would be different than the organization under the Mosaic law. And finally he capped it all off with the following statement:
2 And it came to pass that when Jesus had said these words he perceived that there were some among them who marveled, and wondered what he would concerning the law of Moses; for they understood not the saying that old things had passed away, and that all things had become new.
3 And he said unto them: Marvel not that I said unto you that old things had passed away, and that all things had become new.
4 Behold, I say unto you that the law is fulfilled that was given unto Moses.
5 Behold, I am he that gave the law, and I am he who covenanted with my people Israel; therefore, the law in me is fulfilled, for I have come to fulfil the law; therefore it hath an end. 3 Nephi 15:2-5
It may seem somewhat redundant to us. But the Lord always does things in proper order for the teaching and edification of all.