I've had this cute sock tucked away in my drawer for forever:
Step 1: Make sure the sock will fit your doll's head. No need to get this whole project done only to realize that the sock is too big or too small. That would stink.
Then cut off the top "tube" part of the sock, like this:
Step 2: Serge the top edge or do a zig zag stitch (wide width, short stitch length) around the raw edge to keep it from unraveling.
Step 3: Using sturdy thread, stitch loosely around the cut edge.
Step 4: Pull the thread tight to gather the top of the beanie together and tie the two ends of the thread tightly. Trim edges close to knot or tie in a decorative bow.
And that's it! Now you have a cute little doll beanie!
I also debated about turning it into a skirt...