Mary Oliver is one example of a poet who writes poems addressed to and about animals. For example, her dog Percy is often a subject of her poems. Check out her poem “I Ask Percy How I Should Live My Life” for some inspiration:
Love, love, love, says Percy.
And hurry as fast as you can
along the shining beach, or the rubble, or the dust.
Then, go to sleep.
Give up your body heat, your beating heart.