What about infant baptism?

Grace Communion International (GCI), baptizes adult believers and their infant children. GCI finds support for this in the incarnational Trinitarian understanding of Holy Scripture summarized in this post. A video of an infant baptism ceremony is linked below.

The New Testament speaks of whole households being baptized upon the conversion of that household's head (Acts 16:15, 31-33; 1 Corinthians 1:16). It is likely that there were infants and children in these groups, though these texts do not provide conclusive evidence of infant baptism.

A more persuasive text is Acts 2:39. In Luke’s account of Peter’s speech on Pentecost, Peter speaks of the covenantal promises of God given to believers and their children. In doing so, he verifies that believers' children are already included in the household of faith prior to any personal profession of faith. 1Corinthians 7:14 likewise indicates that the children of believers are in a different category than the children of unbelievers, although neither text specifies exactly what the difference is or how it is to be denoted.

Incarnational Trinitarian theology affirms from Holy Scripture that it is the faith of Jesus Christ, not our own faith, that draws us (Ephesians 2:8; Galatians 2:20 KJV). Christian baptism signifies what God by grace, of his own initiative, has done for us. It is upon the truth of this already accomplished fact that faith comes to rest. As Paul notes, it was “while we were yet powerless” that Christ died for all humanity (Romans 5:6). Christ lived on behalf of all humanity, died for all humanity, and rose again for all humanity. Similarly, he was baptized on behalf of all humanity, and in that way all have been baptized in Christ, whether or not they are old enough to understand that reality. Powerless and helpless humans (adult and infant) are loved and affirmed by God in spite of their current inability to understand or respond.

This video shows an infant baptism service in a GCI congregation.

When adults are baptized they are able to give their free, personal response of faith to God’s claim and call upon their lives. Those who are baptized as infants also come to a point in their lives when they can consciously give their allegiance to Christ. For those who are baptized as infants, a confirmation process provides opportunity to give public acknowledgement of their faith. James Torrance put it this way:
In the practice of infant baptism, we believe that in faith we are doing something for the child, long before the child comes to faith, in acknowledgement of what Christ did for all of us nineteen hundred years before we were born. But in faith we pray that Christ in his faithfulness, and in his own, time, will bring this child to personal faith. The efficacy of baptism is not in the rite or in the water, but in the faithfulness of Christ.
In most churches, infants are welcomed into the community of faith and their special status before God is recognized either by a blessing or by baptism. Either way, the community of faith (parents, extended family, care givers, and all members of the local congregation) have the covenantal responsibility to work together to bring up the child “in the training and instruction of the Lord” (Ephesians 6:4).

Daniel Migliori says this:
While the practice of infant baptism is not absolutely necessary in the life of the church, it may be permissible. And whether it is permissible depends on whether it is being practiced as a routine social rite, or as a form of cheap, magical grace, or instead with the clear understanding that it proclaims the unconditional grace of God in Jesus Christ and calls both parents and community to responsibility for the care, nurture, and guidance of the baptized child in the life of faith, hope, and love. (Faith Seeking Understanding, 2nd ed., p. 286) 
Migliori’s book has an excellent discussion of the permissibility of infant baptism from a Trinitarian theological perspective (including a critique of Karl Barth’s negative position).

When infant baptism is practiced responsibly by the community of faith it can be viewed as a sign of God’s gracious initiative and a powerful expression of the fact that God loves us before we ever begin to respond to him. Infant baptism proclaims that God’s love, grace and salvation are purely his gift. Any human response to this is just a matter of time as to when it occurs.

Given this understanding, GCI baptizes believers and their infant children (when the infant's parents or guardians request it). GCI believes that infant baptism is a scripturally permissible and spiritually blessed expression of God’s unconditional grace and love. As these infants come to faith, they are provided with a confirmation process in which they publicly express their faith in Jesus, providing for them a “rite of passage” that helps mark their conscious acceptance of the grace that has already been given them.