These are the key points:
First and foremost, the axe head needs to be attached to the handle firmly.
The weight of the axe head plays a role in its performance. A massive head offers more force when swinging.
However, a heavy head is only suitable for splitting wood. For carving, you might not go for too heavy an axe head.
It should be ample thin to bite the wood properly and thick enough to ensure durability.
The head should be made from steel that has the right amount of carbon on it.