Monstrumologist by Rick Yancey

Around the turn of the 19th century, Will Henry is an orphan, apprenticed to the doctor with a very unusual specialty:  he hunts monsters. This isn't really what Will Henry signed up for, but it is better than being at the orphanage.  Of course, most of the work happens at night, when the monsters are out and about.  The story begins with a strange man showing up at the back door with a "specimen" that he happened to find in the graveyard at NIGHT (he was grave-robbing).  It is indeed a monster, so the doctor gets very excited and piles everyone into a horse-driven cart to go check out the graveyard AT NIGHT.  Very spooky story with monsters galore, guaranteed to make it hard to go to sleep.  Beginning of a series...