Here's the second prototype. I decided to make it with real paper in case it came out okay! I still want to try a Faberge-like design.
The picture inside the egg and the egg fold together. 
Pop up fully open. 
Here is a pattern for the egg pieces. 
The egg mechanism is called a closed tent. I highly recommend David Carter's book Elements of Pop Up to see these basic mechanisms in action. There are working models built right into the book!