From Nookipedia, the Animal Crossing wiki
The Red Dragonfly (アキアカネ, Akiakane) is a common insect. It can be sold for 80 Bells.
Donating to the Museum
In Animal Crossing
"<Player>, have you ever peered closely into a dragonfly's eyes? Blech! Ghastly, really."
In Wild World
"Ever looked into the eyes of a red dragonfly, or any dragonfly, for that matter? They've "compound eyes," where multiple eyeballs are stuck together, wot! Just think of all those beady little eyes on you! Blech! How very vile... To be honest, bugs with only TWO eyes make me gag."
The Red Dragonfly can be found flying around the second insect room in the museum.
In City Folk
"Since red dragonflies can't regulate their body temperatures, they only come out in the fall. They actually perish when the heat climbs over 86 degrees Fahrenheit. No summer fun for them, wot?"
The Red Dragonfly can be seen in the lower tier of the insect exhibition, flying around the small pool of water in the exhibit closest to the entrance.
In New Leaf
Upon being donated, the Red Dragonfly can be found in the first room of the bug exhibit, flying around the pond and occasionally resting on the fence. The exhibit has this to say about the Red Dragonfly:
"Red dragonflies are seen in the fall, as they're rather sensitive to the heat of summer. They stay in the mountains during the summer and come down to the plains in cooler weather. The males' bodies turn red when they're mature, but their heads and thoraxes are brownish. The females have a more yellowish color and aren't as red as the males, making them easy to tell apart."
The red dragonfly featured in Animal Crossing is most likely a male specimen of Sympetrum flaveolum, colloquially known as the yellow-winged darter. The yelllow-winged darter can grow to be 32-37 mm long, and can be found through the southern half of Great Britain (though not exactly established there), parts of southern Europe, and in central and northern China. Only the males sport the bright red coloration seen in Animal Crossing — females are a golden brown. The species can breed only with stagnant water, such as in peat bogs and still river backwaters. It can be difficult to tell apart the yellow-winged darter from other dragonflies, especially in female specimens.