The Bible is vary vague about baptisms, other than to be baptized. It does not leave instructions, it does not give clear understanding as to what actually happens during baptism, the only crystal clear thing about baptism is that it's commanded. To answer your question, it's important to look into church history to see the development of baptism that we are familiar with today.
Back in the early years, the 0's-300's baptisms were varied and not uniformed. The same can be said for theologies, but that's a different discussion. Mainly, churches had to work with what they had. Baptisms in North Africa looked a lot different than baptisms in Asia Minor, as one can imagine. Because baptisms are largely symbolic, the actual performance, or ritual, of them is not critical. The goal was to mimic Jesus' baptism as much as possible. Running water was preferred, however any water would do, or if water was scarce, sprinkling water was acceptable, and if no water was around sand was considered an acceptable replacement.
Jumping forward, in the first three centuries the largest population getting baptized were adult converts. After the Edict of Milan in 313 that legalized Christianity, the paradigm shifted and most of the population converted. After these converts were baptized, there were no more adults left to be baptized. This is where infant baptisms were first introduce in a large scale. This of course led to more changes in catechumen and the introduction of Confirmation, but to the Early Church, there really was no question about baptizing babies. Parents want their children to be saved, and an aspect of salvation is through Baptism. While I do not believe that salvation is based on Baptism alone, it is a command to go forth and baptize, meaning it's important.
TL;DR: In answering your question, you won't find biblical support for infant baptism because it wasn't an issue when the gospels/epistles/New Testament was written. In the First Century, adults were the only one's being baptized. It was not until later that the Church had to adapt and included infant baptism.
Augustine:
"The custom of Mother Church in baptizing infants is certainly not to be scorned, nor is it to be regarded in any way as superfluous, nor is it to be believed that its tradition is anything except apostolic" (The Literal Interpretation of Genesis 10:23:39 [A.D. 408]).