The Jews had a rite of baptism that including babies, but it was for gentile converts. Jesus wasn't a gentile. And of course, Christian baptism didn't exist when Jesus was a baby (circumcision did, however - and He was circumcised: note WITHOUT His consent, WITHOUT Him first repenting buckets or saying the sinners prayer or doing the altar call thing....)
But, respectfully, I disagree with your premise that we can ONLY do what JESUS did. If you yourself believed your own point, then you'd insist that your church doesn't use electricity or the internet or powerpoint (Jesus didn't)..... That you don't baptize anyone (Jesus never did). That you don't pass Communion around with little cups of grape juice and cut up pieces of Webers' white bread (even giving it to GENTILES!!! Maybe even CHILDREN) - because Jesus never did that. You'd not stand for youth groups or youth pastors or praise bands because Jesus never had or used any of those. And of course you WOULD have the public circumcision of boys 8 days old in church because Jesus was.
- Josiah