Mk. 16:16 is preceeded by verse 15, which reads, "Go into the whole world and preach the gospel to every creature". Hence the statement in verse 16 is related to those who heard the Apostle's preaching. If they listened to the Word of God and believed, they could be baptised. But this does not exclude child baptism. Since Jesus came to save all, children couldn't be denied the right of salvation. The requirement (demand) that unless one is born of water and the spirit, he cannot enter the kingdom of God" (Jn. 3:5) holds good to the children too. They also need a spiritual regeneration through baptism. We are not to obstruct their coming near to Jesus (Cf. Mk. 10: 14-16).
In Bible, we come across a few examples of child-baptism. In Acts 16: 15, it is said that Lydia and her household were baptised. In Acts 16:33, it is said that a Philippian Jailer and all his family were baptised. The terms, household, and family cover all the members including children. Hence we could infer that children were baptised. The Jews used to receive circumcision in the early days of their childhood. Since St. Paul compares baptism to the circumcision one may infer that baptism was made a substitute for circumcision and was given in the early childhood itself. "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, buried with him in baptism, in which you all were raised with him through faith (Col. 2:11-12).
It is proper that children are initiated to faith and given baptism at the early stages itself. If their parents could choose physical nourishment for them, why should we ban their right to choose spirititual nourishment for them? The grown up may walk to the destination by themselves, but the children need their parents to carry them upon their shoulders and take them to the destination. In 1 Pet.3, Peter compared baptism to Noah's ark which saved eight people through the water (VV. 20,21). Let the children also enter the ark (church) and be saved.