Donald did come first, had his "angry streak" show up a year before Daffy (1936, in Mickey's Grand Opera) and Warner Brothers were very much into copying (Looney Tunes were a direct response to Silly Symphonies) but oddly, Daffy was their departure from copying Disney.
To get at what I mean, we need to first visit the Warner Brothers racist Mickey Mouse knockoff.
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Bosko was the brainchild of the animators Hugh Harman and Rudolf Islsing who conceived of it while working as animators at Disney. They made a pilot (Bosko the Talk-Ink Kid) and fished for bids, getting one from Leon Schlesinger at Pacific Art and Title, who had enough of a relationship with Warner Brothers to land a distribution deal.
Bosko was registered with the US copyright office as a "Negro boy", used a thick Southern dialect, and included minstrel qualities, essentially being a direct reference to Al Jolson's blackface character in The Jazz Singer.
While it didn't start that way, once the character really took off for Warner Brothers (showing up in 11 short films in 1931 alone) Bosko became a straight Mickey Mouse ripoff, having a girlfriend named Honey (who was very much Minnie) and dog named Pluto Bruno.
When Bosko left in the summer of 1933 it was due to a money dispute (Harman and Islsing were supposed to receive $10,000 per cartoon but were only getting $7,300) and the empty space on the roster was filled by the short-lived Buddy, who simply Bosko but white.
1935's cartoon I Haven't Got a Hat was the debut of Porky Pig, he of "Th-th-th-that's all, folks!" This catchphrase was used, stuttering-free, by Bosko and Buddy, so he was another attempt at a sort of continuation of the blatant Disney influence. (The stuttering was given to him by Franz Freleng, who thought "it would give him something different, some character".)
Porky was reasonably popular and got top billing, including when Daffy first appeared in Porky's Duck Hunt (directed by Fred Avery, 1937), as Porky has an unsuccessful time hunting, including accidentally shooting a barrel of moonshine and getting some fish drunk who then sing in a chorus. Daffy's portion that led him to stardom was when Porky, thinking he has actually shot a duck, sends his dog to get him; Daffy instead brings the dog back in his mouth.
Porky: Hey, that isn't in the script!
Daffy: Don't mind me, skipper. I'm just a crazy darnfool duck.
Avery originally was going to have a number of ducks, but (at the suggestion of the animator Bob Clampett) settled on just one. He was there specifically to run gags, and as the historian Michael Barrier notes, he had "no trace of Disney" -- nothing "cute" about the character.
This is in contrast to Donald Duck (developed by Dick Huemer for Wise Little Hen from 1934) which was, according to animator Les Clark, “such a feisty little character that Walt liked him right away". Donald's actual first tantrum was thrown, as I mentioned earlier, with Mickey's Grand Opera, while being animated by Dick Lundy, who allegedly was channeling himself.
Daffy's mantle of silly anti-realism gags was never really a Donald staple, and just like with Porky, he seemed destined to be an eternal antagonist and trickster, as most clearly seen with the Chuck Jones short Daffy Duck and the Dinosaur (1939, video here) with Daffy tormenting a caveman who was hunting him. The only reason Daffy shifted a little (and became slightly more Donald-like, but it never was Bosko-copying-Mickey-level) was his star and his schtick was overshadowed by a wisecracking character introduced officially in 1940 (although he appeared once before in an "unofficial" capacity), that of Bugs Bunny.
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Postscript note: there's been some attempt to rehabilitate Bosko, as with the exception of Congo Jazz (1930) he appeared in generally non-stereotypical situations (no watermelon, for example) but he's a long way from making a re-appearance in the canon, as his last showing was in a cameo of sorts in the 1990s movie Space Jam.
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Barrier, M. (2003). Hollywood Cartoons: American Animation in Its Golden Age. United Kingdom: Oxford University Press.
Bendazzi, G. (2015). Animation: A World History. United States: Routledge.
Davis, A. M. (2007). Good Girls & Wicked Witches: Women in Disney's Feature Animation. United Kingdom: John Libbey Publishing.
Ghez, D. (2012). Walt’s People – Volume 12: Talking Disney with the Artists who Knew Him. United States: Xlibris US.
Not really. Donald Duck did precede Daffy by a few years. Donald was created in 1934, and didn't get his first solo cartoon until 1937 ("Don Donald", which also introduced his girlfriend Daisy.) Daffy started as a bit player in a Warner Bros cartoon also released in 1937. But just because they were both ducks didn't mean that one was a direct influence on the other. In fact, Daffy was almost the complete opposite of a Disney character.
Silent cartoons such as Felix the Cat were popular in the 20's, and Disney took animation to a whole new level with the advent of sound and Mickey Mouse. But Mickey was just one of a string of anthropomorphized animals that were used throughout animation at the time. Besides Mickey and Felix, there was Krazy Kat, Oswald the Lucky Rabbit (also a Disney creation) and many more. Cute cartoon animals were easy to animate and made for good toys. Most studios had some form of animal, so a duck character by itself wasn’t all that unique.
In the 30’s, Disney was very successful with Mickey and his subsequent characters. Walt was a filmmaker at heart, and he continuously pushed his studio to make better, more realistic, and more beautiful cartoons. He had better technology, better artists, and bigger budgets. They were certainly the top studio at the time.
The other studios didn't have such big budgets and had to make the best with what they had. Warner Bros was one of these. They started in 1930 as an answer to Disney's success. The studio was run by a guy named Leon Schlesinger. He was a hard-nosed businessman and never spent more money than needed. One notable example of this was that he limited the length of his cartoons to exactly 6 minutes simply because that was minimum length his distributors could accept. God forbid he spend money on a few extra feet of film.
The Schlesinger studios had a couple of units. One of these was run by a director named Tex Avery and had a few young animators - most notably Chuck Jones and Bob Clampett. They were all housed in a rundown shack on the edge of the lot that they dubbed "Termite Terrace". It was in this building that a new type of animation was born. Because they didn't have the resources of Disney, the Warner crews couldn’t compete on visual quality. They had to find new ways to make their cartoons stand out. So, instead of pursuing great art like Disney, they threw convention aside and just went for the laugh.
Daffy was created in this atmosphere. He first starred in Tex Avery's "Porky's Duck Hunt.” Bob Clampett animated him and had a big hand in his creation. While Daffy's first role was small, his character was something completely new in animation. Daffy didn't cater to children. Instead, he was pure anarchy – a wisecracking screwball who was unrestrained and combative. This was a huge contrast to Disney's more sedate characters, including Donald Duck. The only similarity between the two was that they both happened to be ducks.
And Daffy quickly became a success. Bob Clampett soon became a director and used Daffy in a number of cartoons that further stretched the bounds of reality. The studio discovered that wisecracking characters could be more entertaining than Disney's realism. Their cartoons appealed as much to adults as they did to kids, and made just as much money. And Daffy was a big part of that, and one reason why Warner Bros became so successful in the 1940's and beyond.