Final answer:
The imaginary world with its own logic and fantastical events that Alice experiences after following a rabbit down a hole distinguishes 'Alice's Adventures in Wonderland' as a fantasy story.
Step-by-step explanation:
One major characteristic in Lewis Carroll's Alice's Adventures in Wonderland, commonly referred to by the phrase 'Down the Rabbit Hole', that helps identify this as a fantasy story is the presence of an entirely imaginary world with its own unique logic.
The narrative transports the protagonist, Alice, into a world that defies the conventions of our reality, filled with talking animals, peculiar rules, and fantastical events. These traits are quintessential to the fantasy genre, where the narrative often unfolds in imaginary realms with magical elements and creatures unlike those in the real world.