One should not be baptised until after he or she has fully repented. Only those who believe, both the Gospel of the Kingdom of God (the Message Jesus preached), and on Jesus Christ as personal Saviour, can be baptised (see Acts 2:38; 8:37; 16:31).
Children and teenagers have not reached that maturity where they have the self-discipline to truly repent, and believe. When some Samaritans repented at Philip's preaching, "they were baptized, both men and women" (Acts 8:12). Only the adults were mature enough to be ready for baptism.
The average mind does not mature until a person is into their twenties - though there are often exceptions. Some few mature and become sober and serious in life outlook by 18, or on rare occasions, even younger.
An immature mind may experience an emotional feeling of temporary remorse, and this may be falsely construed as repentance when it is only momentary, soon forgotten. It is like "puppy-love". How many teenagers have a number of temporary emotional experiences of feeling sure they are "in love"? Of course they themselves feel sure of it, and generally cannot be talked out of it. Usually, they grow out of it but, in rare cases they may really "know their minds" though this is the rare exception, not the rule. So it is with repentance and belief.
The young person who is baptised may be ever so serious about it at the time. But he or she must meet many temptations peculiar to energetic, dynamic, restless, excitement-craving youth in the blooming flower of sex-appeal. Experience shows a person must be of mature age to be truly converted, and remain converted, and constantly growing spiritually, closer and closer to Christ and His Kingdom.
There can be no set rule about the proper age for baptism. It is almost impossible to be absolutely sure about young people under 21 -- and especially under 18 -- and unless positively sure that such a one has really repented of self-will, self-desire, and the ways of this world, such a one should be encouraged to live according to God's Word, but refrain from baptism until sure. John the Baptist insisted on candidates bringing forth "fruits meet for repentance" - or proving their repentance by the fruits in their lives.
Young people should let a few years of such fruits prove their repentance, and the permanent sincerity and earnestness of their conviction to follow God and His way of life.