Golden Egg #12 is located in Level 1-7: Use the white bird to drop an egg bomb right in front of the concrete blocks behind the slingshot. You can get this Golden Egg in one shot, but sometimes if it may just break the concrete blocks and reveal the Golden Egg. In this case, just use the second white bird to get the egg. (→ see image)
Note, this is a two part video. The first part shows how to find the Golden Egg and the second is a walkthrough on how to pass the actual Golden Egg level.