The molecule above is tryptophan, an amino acid famed as a constituent of turkey meat.
In the body, and in the brain in particular, tryptophan is converted to serotonin (shown below) and then to melatonin (shown at the bottom of this article). Melatonin certainly makes you feel sleepy, and it is sometimes taken by long distance travelers to reset their internal clocks when dealing with time differences. In the United States melatonin is sold as a food supplement, while in Europe it is not as freely available.
However, anyone eating carbohydrates is actually dosing up on melatonin.
And although turkey contains plenty of tryptophan so do chicken, beef, and other meats. So tryptophan is commonly present after a meal. It is carbohydrate molecules and the metabolism of carbohydrates which increases the amount of tryptophan in your brain after a hefty holiday feast. This is because carbohydrate breakdown promotes the transport of tryptophan across the blood-brain barrier.
Although the molecule making you sleepy isn't specifically from turkey, it is tryptophan which makes you sleepy after a large meal.