Actually to steal an egg from the Dragon would exactly be what KAOS would do, it is not a surprise that Drago suspected them. I am sure they would deny it but they never admit to anything.
There is also a theory that it could have been removed to protect the egg and mother from what the Dragon might do. There are animals that are known to kill their own young for either food or in spite. Maybe friends of the Dragon were worried about Drago's state of mind and whisked both the egg and mother away?