According to John Welch, although Jesus gave power and instructions to the disciples to baptize (3 Nephi 11:21-28), these baptisms weren't carried out immediately as the Nephites heard Jesus at this time. Baptisms would have taken far too much time. But they were carried out the very next morning. Some might wonder why they didn't stop at this point to go and actually be baptized. One reason might be that as they had come up to the temple that morning it's quite possible that they had already properly washed and purified themselves, as an Israelite normally would have done in coming up to the temple on a routine day.
This perhaps then gives us one other instance where we might see the old form of washing and purification transformed into the new ordinance or baptism with the coming of Jesus. We know, for example, from excavations around the temple of Jerusalem, dating back to around the second century B.C., that there were mikvaoth or baptismal fonts lining the roads up to the temple so that those who were pilgrims coming to the temple could ritually immerse themselves and be then pure to present themselves at the temple. Those kinds of older forms of washings--which are precedented as early as Exodus 19:10 where Moses told the Israelites to wash their clothes and purify themselves against the day when the Lord would appear to them at Mt Sinai--had now been completely replaced by the true order of baptism which Jesus instructed them in. [John W. Welch, "Christ at the Nephite Temple," in Teachings of the Book of Mormon, Semester 4, p. 134]