Merge / Join two objects to make both move when animating


I am new to blender and I run into some problems when I want to animate my character.
I have two objects (a rabbit and a pair of eyebrows) which I want to join/merge so both will move.
I tried joining the two objects with ctrl+j. However, when I than grab one bone and move it only the rabbit will move and the eyebrows will stay in the same position. My question is how I can join/merge these object in a way that also the eyebrows will move with the rabbit.

You can not join 2 so simply. You now have one object with part his mash controlled by a armature and part of the mesh has no influence over it by the armature you are using.
The answer to the question is in the very basics. You should learn rigging. you need to learn how the influence work.