So our baptism is not like Jesus. Where is it stated that "christian baptism includes babies?
Jesus' baptism was saint John the Baptist's kind of baptism.
Saint Paul recognised that saint John the Baptist's baptism was not Christian baptism.
That is why saint Paul had to baptise the Ephesian disciples despite the fact that John had baptised them before Jesus was crucified.
Acts 19:3-5 He asked, 'Then how were you baptised?' They replied, 'With John's baptism.' (4) Paul said, 'John's baptism was a baptism of repentance; but he insisted that the people should believe in the one who was to come after him -- namely Jesus.' (5) When they heard this, they were baptised in the name of the Lord Jesus,
The church baptises babies for the same reason that God commanded the Israelites to circumcise baby boys.
It is not because babies make a public profession of their own faith.
It is because the babies born into Christian households rely on the faith of the church.
God promises to make them holy.
1 Corinthians 7:14 You see, the unbelieving husband is sanctified through his wife and the unbelieving wife is sanctified through the brother. If this were not so, your children would be unclean, whereas in fact they are holy.