A literary structure

Solution 1:

Today, praise be is an idiom used to give thanks for something. From Merriam-Webster:

—used to say that one is glad or thankful about something

In this case, Walt Whitman is giving thanks to the fathomless universe for the reasons he lists in the second quoted line.

In form, it is an inversion of the common formula, "God be praised" ("Praised be God," or "praised be the universe," or "praised be nachos") which is itself an old-fashioned subjunctive. The American Etymological School Grammar from 1853 felicitously includes an example conjugation of to praise to illustrate this - "I be praised," and so on are all marked the "ancient or poetic form" of the subjunctive, a label that fits Whitman's usage.