Ambrosius

From Muppet Wiki

Ambrosius, Sir Didymus's semi-faithful steed, is a dog who closely resembles Sarah's own dog Merlin. He has much more sense than his enthusiastic master, and knows when to run away from trouble, which usually leads to Didymus chiding him.

The Ambrosius puppet was used in close-ups, while a real dog was used in full-body shots.