Moore lists himself as of the BG William "Bull" Nelson Division, Col. William B. Hazen Brigade, Col. C.D. Pennebaker Regiment, Company E. Matching this with the Civil War Soldiers system places him as a private in the 27th Kentucky Infantry. While Moore does not mention it, he likely saw combat at Shiloh shortly before he died of disease (likely dysentery).
Family records show that William Moore died on June 15, 1862, which is confirmed by Capt. Robinson's letter. Moore's wife Lydia died on July 18, 1862 according to the same family records. They were survived by their infant daughter Harriet who was born on January 23, 1861, and adopted by relatives.
From the guide to the William J. Moore Letters, 1862, (Special Collections, Virginia Polytechnic Institute and State University, Blacksburg, Va.)