The Key is in a form of a human wearing a cloak almost covering most of its body. It is first seen in Chapter 6 where its role is technically a key in opening Caterpillar Lane.
It perished during the incident where the Duke creates a ruckus in Wonderland.
Alice was able to enter Caterpillar Lane when he accomplishes his mission of attaining loyalty from the Queen thus, obtaining the key as his reward.
Alice obtaining the Key as his reward from the Queen
The Mad Hatter asks permission from the Key to enter Caterpillar Lane