Preheat the oven to 325 degrees F (165 degrees C). Grease 2 cookie sheets.
In a large bowl, using a hand-held electric beater, cream together the shortening and sugar until light and fluffy. Add the egg, beat well, and then stir in the vanilla and pineapple. Combine the flour, baking powder, baking soda and salt in a medium bowl, then gradually stir into the creamed mixture. Drop rounded spoonfuls, 2 inches apart, onto the prepared cookie sheets. Bake for 8 to 10 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before removing to a wire rack to cool completely.