Hello there Phrosting,

neat eskimo, what course are you doing?

As you're animating the fur using hair curves select the hair curves and create a collide sphere or cube (Hair > Create Constraint > Collide Sphere/Cube).

The collide object will stop the hair from penetrating the geometry so the fur shouldn't either. You'll need a few of them to cover your character and the collide values will need adjusting to suit your needs.

Once you have your collide objects in place you can parent the various parts to your character skeleton so that they don't get left behind when you come to animate.

Hope that helps,

Mat.