I would think Infant Baptism is best defended by considering how the concept of corporate solidarity through a representative person functions in the Bible.
eg
In most cultures, including the culture of the Bible, the connection between individuals and groups is more closely connected than is the case in our western European culture today.
A person cannot be defined without reference to their being a part of a group.
i.e. a person is understood within the context of their social relationships.
An individual may represent a group when:
1. he is the originator of the group (father e.g. Adam, Levi)
2. he is the authoritative-leader of the group (king / father)
3. his actions affect the character of the group (high priest – making holy
covenant-breaker – making herem)
4. he is the subject of divine will
to bless or curse through him
i.e. he is a divinely ordained representative (e.g. Abraham, David)
Thus when kings and fathers sin, nations and families are usually decreed to be guilty as well.
Among people groups where the family is considered to be a primary unit (of corporate solidarity) under a representative person (i.e. a father), it would be appropriate to baptise the following members of a pagan family accepting the gospel:
(1) the representative person making the profession of faith
(2) persons associated with the representative person who likewise profess faith
(3) persons associated with the representative person yet incapable of making a profession of faith
It would be inappropriate to baptise someone who although associated with the representative person refused to profess faith although capable of doing so.
It would also be inappropriate to baptise someone incapable of making a profession of faith and whose representative person had not made a profession of faith.
If the pagan family accepting the gospel had other children join their household then presumably these also could be baptised even though separated by time from their parent’s own initial profession and baptism.