It wouldn't be a problem to transfer the eggs to a different container as long as the eggs end up in the same position as they were before. If you haven't already you may want to mark the top of each egg to ensure they don't get turned over.
Also, if you setup a sealed egg container make sure the eggs do not come in contact with any liquid water. If any condensation forms on the plastic seal above the eggs be sure to wipe it off before it can drip down on them.