Because of the risk of killing or harming the eggs, i'd tell the person making you move that it would be animal cruelty to move the eggs before they hatch. If they want to argue it, remind them that it's a criminal offense to intentionally harm or kill animals (especially pets), and that you'd be more than willing to summon an officer to talk with them about it.
That would give you at least until the eggs are all hatched to figure out your move and settling down. that and shouldn't you have had some form of warning 2 months in advance that you'd need to move?