The correct answer is option 3 - Earthworm. Earthworms do not undergo periodic moulting of their external body covering.

Moulting, also known as ecdysis, is the process of shedding or replacing the outer covering of the body in animals. It is a common process seen in many animals, including insects, reptiles, and birds, to facilitate growth or to replace old or damaged exoskeletons or skin.

Option 1 - Cockroach: Cockroaches do undergo moulting. They shed their exoskeletons multiple times as they grow and develop.

Option 2 - Cobra: Cobras, like other snakes, also undergo moulting. They shed their old skin in one piece, leaving behind a new, shiny skin.

Option 4 - Dragonfly: Dragonflies also undergo moulting. As they grow, they shed their exoskeletons and emerge as larger nymphs or adults.

In summary, the only animal in the given options that does not undergo moulting is the earthworm.