Use any fabric for the embroidered paper dolls.  Hoop the fabric and appropriate stabilizer together and sew the dolls and clothing.  Then, cut around the doll and clothing closely, being careful not to snip any stitches.

For the hats, you can leave the inside fabric in place, and slice a small area underneath the brim of the hat.  That way the head of the doll can fit through the small slit in the fabric, but the fabric will keep the hat on the doll's head.

If you prefer, you can use small pieces of Velcro as a way to keep the clothes on the doll.  Then, mix and match outfits during a rainy day.  Enjoy!