I'm sorry for your loss. Yes, the IRS says that a child born at any time during the tax year is your dependent for the entire year. Even if born at 11:39pm on new years eve. So when completing the dependent data, make sure you select that the child lived with you "the whole year".

Additionally for your 2018 tax return you'll do the same. You get to claim the child for the entire year, even if they passed away at one minute after midnight on new year's eve.

Again, sorry for your loss.

Just to provide further clarity on "stillborn children can not be claimed". Basically, if you have a "certificate of live birth", the deceased child qualifies to be claimed. Such a certificate is not issued for a stillborn child.

Yes, you can claim your baby on your 2018 taxes.  

A dependent who was born or passed away during the year is considered as having lived with you all year so long as your home was their home when alive. Stillborn children cannot be claimed

Even if the child never made it out of the hospital and into your home, he or she is considered to have lived with you.