Well the Declaration of Independence is just letter telling England go frack yourself.. It did not setup our form of Government. THE CONSTITUTION DID.
The premises of the Declaration of Independence are the heart and spirit of the Constitution. Without those principles you can't even begin to understand anything about the Constitution. You have, as Frederick Douglass said, lost the "ring-bolt to our nation's destiny." His simile was a nautical one: you've lost the connection to the mast that keeps you safe in the severe storm.
The DOI is the fundamental basis for our Country as well as the Constitution, all historians as well as Constitutional scholars recognize that.