Is there an extract you might think of which exemplifies the passage from the Reason of the Augustan Age to the Imagination of the Romantic Age?

I am not sure exactly what you are looking for, but my mind leapt instantly to Wordsworth's Preface to the Lyrical Ballads, the breakthrough volume of Romantic poems he and Coleridge wrote and published circa 1800. If Augustan Age poems were measured, rational and based on great men and Classical history and literature, and sometimes satiric, Romanticism valued emotion, depth of thought and feeling, nature, sincerity  and the common person. A famous extract from the Preface speaks to some of that:
"For all good poetry is the spontaneous overflow of powerful feelings: and though this be true, Poems to which any value can be attached were never produced on any variety of subjects but by a man who, being possessed of more than usual organic sensibility, had also thought long and deeply."
Augustan poets such as Alexander Pope focused on imitating Classical poets such as Horace and Virgil, and writing highly polished pieces. Wordsworth and Coleridge often polished their work, but rejected Classicism in favor of examining and describing their own experiences, including dreams and folk stories. 
I am not supposed to do your work for you, but if you are looking for extracts of poems that exemplify the imagination of the Romantic Age, you might try a poem such as Wordsworth's "The World is Too Much with Us" in which he writes that "getting and spending we waste our power." This poem expresses the Romantic belief in simplicity and the simple life. In his poem "I wondered lonely as a Cloud," Wordsworth engages in a typical Romantic praise of nature and says "wealth" comes to him when he watches thousands of daffodils waving in the breeze. A glance at his Lucy poems will show how he focuses on simple cottagers rather than high born aristocrats. I hope this helps. Essentially, the Preface to Lyrical Ballads and the poems in that volume are the place to start to document the passage to a Romantic sensibility.