A good thing I learned the other day. If u are in dangerous territory but need wood, pick up your beaver with an argentavis and fly towards the base of a tree. When you reach the tree fly slowly straight up the trunk and the beaver will collect the tree on its own. No need for wander or anything crazy. I suggest whistling neutral once your out and about incase some bugs get frisky. Rare but it happens.
These things are amazing! If you find a wild one, then that’s great because you can raid it’s dam for some cementing paste. Now, if you tame one, the beaver sadly won’t make any dams. But, you can now harvest a bunch of wood with it if you put it on wandering or use a saddle. If you think it’s a bit dangerous running on the ground, let me introduce you to one of the greatest things in this game for gathering, auto-harvest. Just get an argentavis and it’s saddle, grab a tamed beaver, and go up to a tree and let the beaver hit it. ( Put on wandering for the beaver for it to work) This is way safer than being on the ground. To get way more wood, put some levels into melee and even weight if you want to. Auto-harvest also works with ankylosaurus and doedicurus.