(The only way I did this is by going to the place where you get the hammer in the beginning when you're prgressing throught the game. I'm not sure if you can do this later after you return to Goomba Village with the hammer and without the doll.)

Go to the place where you got your hammer. Try to use your hammer on every tree (possibly try the one on the far right). On one of the trees, a doll should fall out of it. It is Goombaria's doll! Return it to her and she'll give you a Star Piece.