Warning: Contains mild content, viewer discretion advised :)
It's just personal opinion. As a former Boy Scout (not bragging), I would bring:
1. Beaver Traps, to set up extras after checking your traps.
2. Bowie Knife, to skin the beavers.
3. Bullet Pouch, to hold bullets.
4. Powder Horn, to shoot a gun.
5. Gun, to kill any dangerous and wild animals.
6. Hatchet, to skin/kill a beaver.
7. Lantern, to use while in dark areas or at night time.
8. Bait for Beaver Traps, to use for beaver traps after failed or caught beavers.
9. Journal and Pencil, to keep record of how many successful traps.
10. Map, to navigate each trap.