Assigning to .order on instances of EulerRotation is a functional way to, for example, change the solutions yielded by the asMatrix() method. It's therefore a functionally significant attribute, and I would have expected it to persist after a copy() operation:
import pymel.core as p
originalRotation = p.datatypes.EulerRotation([0, 1, 2])
originalRotation.order = 'ZXY'
print(originalRotation.order)
# 'ZXY'
rotationCopy = originalRotation.copy()
print(rotationCopy.order)
# 'XYZ'