In large bowl, cream together butter and brown sugar. Beat in egg and vanilla.
In medium bowl, stir together flour, baking powder, baking soda and salt. Gradually add flour mixture to butter mixture until just combined. Knead in chopped pecans. Wrap dough with plastic wrap and chill for at least 30 minutes.
Preheat oven to 350°F.
On lightly floured surface, roll out chilled dough until just under 1/4 inch thick. Using dove-shaped cookie cutter that has been lightly dusted with flour, cut out cookies. Re-roll scraps as necessary. Bake cookies on ungreased cookie sheets for 6-8 minutes or until golden brown around edges. Remove to wire racks and let cool.
Measure out 1 teaspoon of chocolate chips and set aside. In microwave safe bowl, stir together remaining chocolate chips and oil. Microwave on high for 15 seconds. Stir, then repeat 2-3 times more or until chips are melted and smooth.
Line cookie sheet with wax paper or foil. Dip one side of pecan halves 1/3 of the way into melted chocolate. Place on prepared cookie sheet and allow to set in cool place.
Reheat remaining chocolate if necessary to mark eyes and tails. Spoon into pastry bag or sealable plastic sandwich bag. Snip off small hole in tip and pipe over tails of doves, then pipe small lines as neck bands, dab a dot for the eyes and pipe over beaks if desired. Adhere reserved mini chocolate chips to the eyes while chocolate is still wet.
In small saucepan over medium low heat, stir together caramel bits and milk. Cook until caramel is melted and smooth, stirring often. Working with a few cookies at a time, spread caramel over wings. Adhere pecan halves to wings, with chocolate edges on outer side of wings.