1. Baptisms should be done in the presence and oversight of a local church. In the Great Commission (Matthew 18:16-20), Jesus commands to “go and make disciples” he also assures them that he is with you…PLURAL. Jesus gave his authority and command not to each one individually, but to all of them collectively. The group would eventually become the local church. Paul points out that Jesus died for the CHURCH in Ephesians 5:25. Do not underestimate the importance of Christian community in this ordinance. The local church is also pointed to as the pillar and support of the truth in 1 Timothy 3:15. Note: Mission field examples may be an exception if no local church exists yet.
2. Baptisms must have pastoral oversight. +Baptizing is not explicitly given in the commands for elders/pastors in 1 Timothy 4 or any other passage in the New Testament. However, based on the fact that this ordinance belongs to the local church, the pastor/elders are overseers. It stands to reason that they would be overseers in this area.
3. All examples in the NT, except one, are performed by someone holding an office of the local church. The only example of someone performing a baptism that was not set aside for an office of the church was Ananias. Please keep in mind that this may not have been a unique event in the history of the church, descriptive instead of prescriptive. Here are the accounts in chronological order:  Acts 2:41;  Acts 8:12;  Acts 8:13;  Acts 8:36-38;  Acts 9:5,9,18; (cf. Acts 22:16)  Acts 10:44-48;  Acts 16:14,15;  Acts 16:31-33;  Acts 18:8 (cf. I Corinthians 1:14-16);  Acts 19:1-7. Baptism is also mentioned in Acts 1:5, 22; 10:37; 11:16; 13:24 -- all in reference to John’s baptism.
While the Bible does not specifically answer the question, I believe that the safest course of action is for pastors/elders to perform this ordinance. Since all the NT examples, with the exception of one, are performed by those who are set aside for offices of the church either apostles, elders/pastors, or evangelists. +It may be possible for exceptions to be made under pastoral oversight, as there is no hard and fast biblical teaching that exactly answers the question in clarity. Although pragmatically, it is simpler for a pastor or perhaps deacon to perform this ordinance, simply because the person who is perfuming the baptism represents the local church in her authority to perform this function. The church will need some way of affirming the person performing the baptism, and that would often add extra steps. Let me give you one more reason it may be better for a pastor to perform a baptism. As a Southern Baptist, we have always viewed baptism as obedience to the command of Christ, and entrance to the body. Given the individualistic/self-centered culture, we find ourselves living in, it may show more community support for the pastor to perform instead of a family member or friend.