Carpenterbugs can be found in a variety of places. The Tundra and Flooded Forest areas possess them, but the earliest you can encounter them is in the Moga Woods. Be sure to equip good gathering equipment (the starting Hunter set isn't bad) as well as food buffs and head to Area 4 (the Giggi cave). Off to the side, there's an alcove with Felynxes and Melynxes. There's a bug gathering spot in the center where you can find Carpenterbugs. I've personally gathered at least Carpenterbug each time when decked out properly and have received upwards of 4 in one run.