Everything that Jesus said and did is not recorded in the Gospels. So though there are not recorded specific instances of Jesus baptising others,we simply don't know how many or who He baptised, or if He baptised others at all. We do know, however, that He Himself was baptised.
He never, not once, told His followers to refrain from baptism or from baptising others. The practice of the first generation of Christians was to baptise and be baptised. The New Testament is filled with examples of just this, as well as directives to be baptised.
So why would someone who COULD be baptised refuse to be baptised? Please answer this question.
Acts 8:35 Philip opened his mouth, and beginning at this Scripture, preached Jesus to him. 36 Now as they went down the road, they came to some water. And the eunuch said, “See, here is water. What hinders me from being baptized?” 37 Then Philip said, “If you believe with all your heart, you may.” And he answered and said, “I believe that Jesus Christ is the Son of God.” 38 So he commanded the chariot to stand still. And both Philip and the eunuch went down into the water, and he baptized him.
36 “Therefore let all Israel be assured of this: God has made this Jesus, whom you crucified, both Lord and Messiah.”
37 When the people heard this, they were cut to the heart and said to Peter and the other apostles, “Brothers, what shall we do?”
38 Peter replied, “Repent and be baptized, every one of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the gift of the Holy Spirit.
39 The promise is for you and your children and for all who are far off—for all whom the Lord our God will call.”
40 With many other words he warned them; and he pleaded with them, “Save yourselves from this corrupt generation.”
41 Those who accepted his message were baptized, and about three thousand were added to their number that day.
Acts 10:47 “Can anyone forbid water, that these should not be baptized who have received the Holy Spirit just as we have?” 48 And he commanded them to be baptized in the name of the Lord. Then they asked him to stay a few days.
Acts 16:33 And he took them the same hour of the night and washed their stripes. And immediately he and all his family were baptized.
Acts 22:16 And now why are you waiting? Arise and be baptized, and wash away your sins, calling on the name of the Lord.
Acts 9:18 Immediately there fell from his eyes something like scales, and he received his sight at once; and he arose and was baptized.
Acts 8:12 When they believed Philip as he preached the things concerning the kingdom of God and the name of Jesus Christ, both men and women were baptized. [Mentioned again in verse 16.] 13 Then Simon himself also believed; and when he was baptized he continued with Philip, and was amazed, seeing the miracles and signs which were done.
Acts 16:15 And when [ Lydia ] and her household were baptized, she begged us, saying, “If you have judged me to be faithful to the Lord, come to my house and stay.” So she persuaded us.
Acts 18:8 Crispus, the ruler of the synagogue, believed on the Lord with all his household. And many of the Corinthians, hearing, believed and were baptized.
Romans 6:3 Do you not know that as many of us as were baptized into Christ Jesus were baptized into His death? 4 Therefore we were buried with Him through baptism into death, that just as Christ was raised from the dead by the glory of the Father, even so we also should walk in newness of life.
1 Cor. 12:13 By one Spirit we were all baptized into one body—whether Jews or Greeks, whether slaves or free—and have all been made to drink into one Spirit.
Colossians 2:11 In Him you were also circumcised with the circumcision made without hands, by putting off the body of the sins of the flesh, by the circumcision of Christ, 12 buried with Him in baptism, in which you also were raised with Him through faith in the working of God, who raised Him from the dead. 13 And you, being dead in your trespasses and the uncircumcision of your flesh, He has made alive together with Him, having forgiven you all trespasses.
1 Peter 3:20 . . . In the days of Noah . . . the ark was being prepared, in which a few, that is, eight souls, were saved through water. 21 There is also an antitype which now saves us—baptism (not the removal of the filth of the flesh, but the answer of a good conscience toward God), through the resurrection of Jesus Christ.
Ephesians 4:4 There is one body and one Spirit, just as you were called in one hope of your calling; 5 one Lord, one faith, one baptism, 6 one God and Father of all, who is abov e all, and through all, and in you all.
Hebrews 10:22 Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience and our bodies washed with pure water.
Ephesians 5:25 Husbands, love your wives, just as Christ also loved the church and gave Himself for her, 26 that He might sanctify and cleanse her with the washing of water by the word , 27 that He might present her to Himself a glorious church, not having spot or wrinkle or any such thing, but that she should be holy and without blemish.
1 Corinthians 6:9 Do you not know that the unrighteous will not inherit the kingdom of God ? . . . 11 And such were some of you. But you were washed, but you were sanctified, but you were justified in the name of the Lord Jesus and by the Spirit of our God.
Titus 3:5 Not by works of righteousness which we have done, but according to His mercy He saved us, through the washing of regeneration and renewing of the Holy Spirit.
As I've stated repeatedly - baptism does not save us. But clearly baptism is an important step of obedience.
So - be baptised. It's not like it's difficult to do - or to understand.