Few things in life are more joyous than the arrival of another new baby in the family. Among the necessary tasks is a review of your estate planning documents. If you had a will prepared for your first child, it is possible that the existing documents simply need to be updated. But don't wait. Make sure that you also address guardianship issues, should anything tragic occur in your family.
In the post "Will another baby affect your current will?"New Jersey 101.5 advises checking on your will to see whether it identifies your "children" or "descendants" as your beneficiaries—and then defines those terms to provide that children born after you executed your will are included.
If it does, then it is probably not urgent to update your will to include your new child's name. However, if the will was drafted without that flexibility and only identifies your first child by name as the beneficiary, then you need to talk with your estate planning attorney and have your will updated.