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Douglas Harper's Etymology Dictionary
bird-brain

also birdbrain, 1936, slang, "stupid person," also perhaps suggestive of flightiness, from bird (n.1) + brain (n.).

Wikipedia
Bird-Brain

Bird-Brain is a fictional character appearing in American comic books published by Marvel Comics.

Usage examples of "bird-brain".

But it's time you bird-brained dopes realized that you have been outlawed.

While I can understand Felaras not wanting every bird-brained flitter-head in the Order to go flying off on tangents because of a little bad news, I rather resent that she feels she needn't tell those of us who are levelheaded until she's ready for us to hear things.

Not the family bird-brain, who was on patrol now, or, more likely, hitting on some nitwitted pigeon.