There's two ways I like to work with hair: building it from simply shapes (which can create some bizarre and fun styles) or drawing it our with the Paintbrush Tool (B) or Blob Brush Tool (Shift-B). In this step, we'll build a hairstyle from circles.
Create a new layer and name it "Hair". Make sure it's above the base body in the Layers panel. Using the Ellipse Tool, draw an ellipse that overlaps the doll's forehead. Select the base body's head (use the Direct Selection Tool so you don't have to ungroup) and select the ellipse. Use the Shape Builder Tool (Shift-M) to select the non-overlapping portion of the ellipse. Deselect (Shift-Control-A) and lock the base body layer in the Layers panel.
Use the Direct Selection Tool (V) to select the extraneous component of the ellipse and delete it.
Draw a large circle around the doll's head that overlaps her chin.
Copy (Control-C) and Paste (Control-V) the circle and move it down and to the right.
Select both circles and hit Minus Front in the Pathfinder panel.
Select the new shape you've made, Copy, Paste, and Reflect it over a vertical axis.
Align the right side of the hairstyle with the left and Unite all three pieces in Pathfinder.
If you like this kind of bobbed hairstyle, you can continue to use it and build others with basic shapes using the Shape Builder Tool and the Pathfinder panel. However, if you're like me, you'll want your doll to have hair that looks less molded and more like rooted hair.