From Nookipedia, the Animal Crossing wiki
The Walking Leaf (コノハムシ, Konohamushi) is an uncommon insect that was introduced in Animal Crossing: City Folk. They are found from July to September, from 8 a.m. to 5 p.m. and can be found in all weather (rain and sun). They camouflage themselves as furniture leaves (though appear a lighter shade of green) on the ground, but when approached they will flip over and reveal themselves. They are sold for 600 Bells.
Donating to the museum
In City Folk
After donation, the Walking Leaf can be found on the middle-terrace of the insect exhibition, in the central enclosure near the eastern-most tree stump, sharing its enclosure with the Grasshopper.
In New Leaf
Upon donation to the museum, the Walking Leaf can be found in the upper right corner of the upper right room of the Insect section. The exhibit has this to say about the Walking Leaf:
Bug encyclopedia information
Walking leafs can disguise themselves so well that some even show signs of fake bite marks, to further confuse predators. When they walk, they sway to mimic a leaf being rocked by the wind. They can be found in South/Southeast Asia to Australia.
Names in other languages