I'm sorry for your loss. You can claim the baby as a dependent for the entire year provided a certificate of *live* birth was issued. (If the baby was stillborn and no certificate of live birth issued, then you have no claim unfortunately)
When filling in the dependent information there will be a checkbox on one of the screens for "Passed away in 2017" Make sure you select that box and enter the date of his passing below that.
Finally, you most likely do not have an SSN for the baby. That means you can not e-file your return if you desire to take the exemption. You will have to print it, sign it and mail it to the IRS. On the screen that asks for the baby's SSN, enter the word DIED in all caps, and then you can continue to the next screen.
