Except the "unique formulation of the Declaration" is "Life, Liberty and the pursuit of Happiness", not just "happiness". To mean the same thing the words should be "Life, Liberty, and the pursuit of Property".
Life and Liberty are inherent to a human being. Happiness and Property are not. They must be pursued and attained. We have a right to pursue them but no guarantee that the pursuit will be successful.
The right to life is the supreme right, intrinsically. Without it, you can never enjoy your rights to liberty or private property. But the latter two are God-given and unalienable too.