From Muppet Wiki

Sir Didymus is a fox-terrier in Labyrinth, as specified by the presskit, who believes he is a great and chivalrous knight. He has a canine steed named Ambrosius, and has the job of guarding the bridge that crosses over the Bog of Eternal Stench.

Didymus is brave to a fault, being the first to rush into a dangerous situation and the last to back out (if he ever does back out), with no regard at all to personal safety. He follows a strict chivalraic code and once he sets his mind to something, one would be hard-pressed to get him to stop (although asking nicely seems to work).

Didymus is not one of Jareth's underlings. After some persuasion from Sarah, he and Ambrosius joined her group of comrades, referring to her as "my lady."