For follow-up discussion and general commentary on the topic. Comments are sorted chronologically.
Is it proper to baptized a new born baby?
Baptism is a ceremony whereby a person publically declares he or she has come to a saving faith in Jesus. Biblically speaking, baptism is performed by immersing a believer in water and not by pouring or sprinkling water on their body. It is important to note that baptism does not save a person as salvation comes by confessing Jesus as Lord and Saviour (Romans 10:9).
As a baby cannot understand what baptism is about nor are they able to confess Jesus as Lord and Saviour, it is evident that infant baptism is not biblical.
If baptized as a baby, is it necessary to be baptized when reaching the age of reason?
It is not 'necessary', as in required or commanded, to be baptized with water again. However, you can certainly choose to do so if you do not feel the first counted, and wish to personally give a testimony before men. Parents were allowed to baptize their children in the Bible, even if the children did not yet believe (Acts 16:33, I Cor 1:16, Acts 16:15). This is perhaps because it is the head of household that sets the spiritual direction of the household (Josh 24:14-15), and that unbelieving family members are set apart for the sake of the believers and the children counted as holy (I Cor 7:12-14).
As such, whether to get baptized again is a matter of conscience and personal conviction. You can simply declare that the childhood baptism was valid (you agree with the public testimony of Christ that your parents made then), or decide to get re-baptized with a public testimony of your own. You should not feel you "must" get re-baptized for it to count, but neither should you feel that you "have" to accept the infant baptism if you do not feel it was valid or sufficient.