Queen Tyrani, known better as the Martian Queen, does not appear in the original "Looney Tunes" shorts, but rather as a regular on the animated series, Duck Dodgers, based on one of those shorts. The white-haired Martian beauty is the ruler of Mars, and is obviously of the same species as her army commander, X-2 (alias Marvin the Martian), who works for her.
The Queen's name comes from the word "tyranny", which is mentioned right at the moment she appears in the show's theme song.
Tyrani was first seen in the series premiere, "The Trial of Duck Dodgers", and due to a misconception, she believes that Duck Dodgers (Daffy Duck) is what he claims to be - the most brilliant tactical mind in the universe.
By the episode "To Love a Duck", Tyrani has an obvious crush on Dodgers, and so has him captured because she wants him to be her king. This upsets X-2, who has a crush on the Queen himself. In the series of tests the Queen organizes for Dodgers to prove his worthiness, X-2 continually tries to harm Dodgers' progress, but to no avail. Eventually, X-2 tricks Dodgers into abandoning the idea by lying to him about the duties the King of Mars would have.
Tyrani is rather upset about being abandoned at the altar, and in a later episode, "The Queen Is Wild", she tries to lure Dodgers into being killed by kidnapping the Eager Young Space Cadet (Porky Pig). In the end, though, Tyrani spares Dodgers, as she still has feelings for him.
Tyrani apparently still has a crush on Dodgers, even after being told by I.Q. High that he's not exactly what she sees him as ("Deconstructioning Dodgers"). However, as of the two-part episode "Of Course You Know This Means War and Peace", she is now aware of X-2's crush on her. They even planned to wed in the episode "Till Doom Do Us Part". By the end of the episode, though, her rather strong feelings for Dodgers are rekindled, and she cancels the wedding.