The Declaration of Independence has no legal authority whatsoever, since it is not part of the Constitution, nor was it passed bu the Congress under the Constitution.
You are correct that the Declaration did not establish the form of government that the people of the United States chose to institute for themselves, from which the rule of law would flow.
That said, what I cited was the preamble to the Constitution, with references back to the Declaration in an attempt to enlighten the thinking behind the meaning of the words used in the preamble in the Constitution.
-PJ