Moore did something poets almost never have the opportunity or ability to do: she invented a whole new architecture, a new and describable prosodic system. You could argue that two poets did this in the 19th century: Gerard Manley Hopkins and Walt Whitman. But with these two marvelous poets the case seems less clear-cut, since the rules of Hopkins's "sprung rhythm" can be arcane and hard to follow, even for his devotees, and Whitman's system isn't strictly speaking systematic: it would be hard to agree upon its operating usages or to predict how it will proceed. (You could also argue that Longfellow's Hiawatha represents a new system, but I don't care enough about the poem--prosodically curious though it is--to litigate on its behalf.)
But even if we include both Hopkins and Whitman with Moore, it's still apparent just how rare and difficult is this phenomenon where a poet redesigns the basic blueprints of what a poem can be. (From a taxonomic point of view, nearly all English-language poetry can be classified under a mere half-dozen or so prosodic systems.)
To introduce radical shifts in content is a much more common occurrence. You pick up Wordsworth's The Prelude and you say to yourself, "Before him, no English poet ever wrote about childhood in this way" (even as you note that the poem's basic building-block is our old friend--our very old friend--blank verse). Likewise, to introduce radical shifts in tone--the ear-quickening sound of a new timbre--is comparatively common. To venture as a reader from the plod and solemnity of Byron's Childe Harold (completed 1818) to the dash and irreverence of Don Juan (its first two cantos published in 1819) is to see that similar content can be utterly transformed with a change of voice. Everything's the same and yet different, it's all shockingly modern, as Byron suddenly becomes "our" Byron (even as we observe that the two poems are, structurally, all but identical).
Moore's system is known as syllabic verse, but she was hardly the first poet to count syllables and to let stresses fall where they might. What she managed to do was to bring to syllabic verse a complement of additional poetic techniques: an idiosyncratic array of indentations, an eschewal of capital letters, a blurring of title and text, a dependence on subtle and off-beat (literally off-beat) rhymes, etc. Together these tools helped to create a complicated and charming verbal contrivance of a sort that English hadn't seen before. Moore wrote some gorgeous poems throughout her career, but it was chiefly in the late thirties and early forties--with a too-small handful of lyrics like "Nevertheless" and "Bird-Witted" and "What Are Years"--that all her prosodic virtues cohered. These are not merely beautiful poems but peculiarly exciting poems. They come to us like the trailing echoes of some vibrant party in the next room--a room that is doubtless a glittering salon, though we can't actually glimpse it, quite. But we know its conversation is richer and more rarefied than that of any party we've ever actually attended.
Moore's system feels capacious; you get a sense that others can profitably work within it. In this, she's different from a contemporary she deeply admired, cummings, who was likewise a prodigious innovator but most of whose innovations prove effective only within his own hands. Poets attempting to borrow from cummings almost always wind up sounding like bad cummings. (And the fact is, he wrote enough bad poetry without our adding to it.) When W. H. Auden or Elizabeth Bishop composes a poem unmistakably influenced by Moore, there's every likelihood that the poem will nonetheless seem a genuine Auden or Bishop poem.
It's impossible to say when another poet will come along who offers such transformations at the root of things--at the prosodic mainstays and foundations. And equally impossible to predict what such innovations might look like. But I hold out hope for new patterns--patterns which, if sufficiently, boldly new, will probably at first not look like patterns at all.