Below I have posted an excerpt from Easton's Bible Dictionary. I found it to be a rather helpful article. I hope it is helpful for others too. As I said yesterday I will begin in a few days to discuss "Believers Baptism," and the arguments in favor of that view.
2. In support of the doctrine of infant baptism, i.e., of the baptism of the infants, or rather the "children," of believing parents, the following considerations may be adduced:
The Church of Christ exists as a divinely organized community. It is the "kingdom of God," one historic kingdom under all dispensations. The commonwealth of Israel was the "church" (Acts 7:38; Rom 9:4) under the Mosaic dispensation. The New Testament church is not a new and different church, but one with that of the Old Testament. The terms of admission into the church have always been the same viz., a profession of faith and a promise of subjection to the laws of the kingdom. Now it is a fact beyond dispute that the children of God's people under the old dispensation were recognized as members of the church. Circumcision was the sign and seal of their membership. It was not because of carnal descent from Abraham, but as being the children of God's professing people, that this rite was administered (Rom 4:11). If children were members of the church under the old dispensation, which they undoubtedly were, then they are members of the church now by the same right, unless it can be shown that they have been expressly excluded. Under the Old Testament parents acted for their children and represented them. (See Gen 9:9; 17:10; Ex 24:7,8; Deut 29:9-13.) When parents entered into covenant with God, they brought their children with them. This was a law in the Hebrew Church. When a proselyte was received into membership, he could not enter without bringing his children with him. The New Testament does not exclude the children of believers from the church. It does not deprive them of any privilege they enjoyed under the Old Testament. There is no command or statement of any kind, that can be interpreted as giving any countenance to such an idea, anywhere to be found in the New Testament. The church membership of infants has never been set aside. The ancient practice, orginally appointed by God himself, must remain a law of his kingdom till repealed by the same divine authority. There are lambs in the fold of the Good Shepherd (John 21:15; comp. Luke 1:15; Matt 19:14; 1 Cor 7:14).
"In a company of converts applying for admission into Christ's house there are likely to be some heads of families. How is their case to be treated? How, for example, are Lydia and her neighbour the keeper of the city prison to be treated? Both have been converted. Both are heads of families. They desire to be received into the infant church of Philippi. What is Christ's direction to them? Shall we say that it is to this effect: 'Arise, and wash away your sins, and come into my house. But you must come in by yourselves. These babes in your arms, you must leave them outside. They cannot believe yet, and so they cannot come in. Those other little ones by your side, their hearts may perhaps have been touched with the love of God; still, they are not old enough to make a personal profession, so they too must be left outside...For the present you must leave them where they are and come in by yourselves.' One may reasonably demand very stringent proofs before accepting this as a fair representation of the sort of welcome Christ offers to parents who come to his door bringing their children with them. Surely it is more consonant with all we know about him to suppose that his welcome will be more ample in its scope, and will breathe a more gracious tone. Surely it would be more like the Good Shepherd to say, 'Come in, and bring your little ones along with you. The youngest needs my salvation; and the youngest is accessible to my salvation. You may be unable as yet to deal with them about either sin or salvation, but my gracious power can find its way into their hearts even now. I can impart to them pardon and a new life. From Adam they have inherited sin and death; and I can so unite them to myself that in me they shall be heirs of righteousness and life. You may without misgiving bring them to me. And the law of my house requires that the same day which witnesses your reception into it by baptism must witness their reception also'" (The Church, by Professor Binnie, D.D.).(from Easton's Bible Dictionary, PC Study Bible formatted electronic database Copyright © 2003 Biblesoft, Inc. All rights reserved.)