Unity2D: How to make an object pick up another object and carry it around?

I need a little help guys. I am brand new to Unity and developing my first 2D game.

In my game, I am trying to make a bird pick a stick from the ground in her beak, fly around with it still attached to her beak and put it down somewhere else. I am rotating the bird back and forth (z-axis). When the bird's beak touches the stick object on the ground the stick should automatically attach itself to the bird's beak. The bird currently flies (my only achievement so far :P), and it should also be able to fly around with the stick in her beak. And lastly, the bird should be able to place the stick in a predetermined place (building nest). So when putting the stick on this predetermined place the bird will rotate down (z-axis) making the stick touch this predetermined space which is when the stick should de-attach and place itself in this predetermined area.

I have been trying to figure out how to implement this "object sitting on the ground when touched attach itself to a specific point of another object" all day long and couldn't come up with a solution. Maybe I am overthinking this.

Any solutions, directions, pointers? Simple the better!