So sorry for your loss, yes you can claim your child, a child born during the year and that passes away during the year is deemed to have lived in your home for the entire year.  Select the child lived with you all year when you enter their information on your tax return.

Also, see the following from the IRS:

Born and died in 2016.   If your child was born and died in 2016, and you don’t have an SSN for the child, you may attach a copy of the child's birth certificate, death certificate, or hospital records instead. The document must show the child was born alive. If you do this, enter “DIED” in column (2) of line 6c of your Form 1040 or Form 1040A.