I ordered fake eggs online, but the eggs they sent me were smaller than the dove eggs. They seemed to do the trick ok, but I ended up making some from FIMO, ( a craft clay that you harden in the oven) that were the same size as the real dove's eggs. It's really easy.
I would say your two Doves are particularly tame. They are easy to tame but they do not come out of the egg that way. They need to be handled regularly from a young age to become as tame as yours are. You really did hit the lottery! I would caution you about jumping right into breeding, however...