Much later after Jesus' water baptism, Jesus said, "But I have a baptism to undergo, and how it consumes me until it is finished!" Luke 12:50 (CSB). What baptism was this? It was a baptism of Jesus' will and life to obey God's will unto death. All who want to follow Jesus are baptized into His death as well. "Therefore we have been buried with Him through baptism into death, so that as Christ was raised from the dead through the glory of the Father, so we too might walk in newness of life," Romans 6:4 (NASB). This is our true baptism into Christ.
The symbolic baptism of water immersion is only an outward representation of our covenant with God. A person is lowered backwards into water (symbolizing the death of his will/life) and raised up out of the water to a new life of obeying God's will. Thus, water baptism is not the true baptism. It only symbolizes it.
Therefore, the performance of this symbolic act may be by a woman, an unconsecrated believer, or even by a worldly person. The real contract between the Lord and the individual has already occurred.
In the New Testament, usually male elders immersed new believers. Their Christian maturity would add solemnity, wisdom and encouragement to the experience. But, since there are no specific scriptural directions as to who may perform this symbolic service, anyone could do the immersing. The identity of the immerser, whether even a good or bad person, would not invalidate a baptism. The immerser acts merely as a representative for the convenience and service of the new Christian. (See Studies in the Scriptures, F455.)