I love the way young people think they invented language, especially pejorative terms.
Liked nobody cursed before 1989.

I did a double take when I heard that, too! I figured it was a mistake of some kind, but when I saw your post here I looked it up and was surprised to find the term being used before 1900
https://books.google.com/ngrams/graph?year_start=1800&year_end=2008&corpus=15&smoothing=7&case_insensitive=on&content=douchebag&direct_url=t4%3B%2Cdouchebag%3B%2Cc0%3B%2Cs0%3B%3Bdouchebag%3B%2Cc0%3B%3BDouchebag%3B%2Cc0

George Carlin, from New York, said 'douchebag' was slang for any female: 'He brought two douchebags with him.' Maybe it then became an insult in the 60s, when I first heard it used as an insult, you douchebag.

i was a little surprised as well. The first time i ever heard it as an insult was Revenge of the Nerds (1984), where Booger says Stan Gable looks like his mom's old douchebag, but even there he wasn't calling him a douchebag outright, just comparing him to one I bet its a New York thing.

Its possible it was used as a pejorative term as early as the 1930s or 40s although it appears it wasnt widely used as an insult until the 1960s.
The 1951 classic novel
From Here to Eternity
by James Jones used it as an adjective;
The trouble with you, Pete, the voice that did not seem to come with him but from that cigaret said savagely, is that you cant see further than that
douchebag
nose of yours.

It's used in another Allen film 'Radio Days' set in the early 1940s too.
"I re-evaluated our lives. I got a 10, you got a 6"

I'm infinitely more interested in the answer to this question, regarding it's use in the mid-1930s, even though I originally was wondering the same thing as the OP.
"Who do you think you are, Bill Clinton? You're a comptroller!"

Not to quibble, but the real question is: did the term exist, and was it widely used as an insult, in the mid-1930s, when the movie is set?
We know it existed when the movie was made, since it's there.