I'd probably make 2 long tubes of fabric and leave them unstuffed. You might even want to sew some sort of weight into the ends of each tube. Folded in the middle these could be the legs and the arms.
Then I'd make a stuffed body of some sort. Maybe sew on buttons for the eyes. Add ears if you want to make it a rabbit or a mouse, etc. Attatch the arm tube near the middle and the legs at the bottom.
Then cross some sticks and lash them together. Attatch a string to each arm and each leg. Also attatch a string to the top of the head. Finding the length for the strings is the hardest part. You want them to hang in place when the sticks are horizontal. Tie the string on it's head to the crossed part of the sticks. Tie each arm to a stick end and each foot to a stick end.