I have researched early military photography for a few years online and have found there is no conclusive list of the earliest combat photography and so I have set out to make one. Combat photography can be differentiated from other types of war photography in that the action of battle can be seen occurring in the photograph. The first war photography took place in the Mexican-American War (1846-1848) by an anonymous photographer, but it wasn't until the American Civil War (1861-1865) that the first combat photos were taken. Because of the limitations posed by the time and complexity it took to take a photo in the mid-to-late 1800's made it difficult to obtain images during battles but a few of naval actions did emerge. There was also not a tradition of journalists and artists putting their lives on the line for an image. The overall amount of combat photography before World War One was small, but a few images did emerge from a few courageous and pioneering people. By the time of World War One governments saw the value in having large numbers of photographers to document conflicts for propaganda purposes and improved camera technology allowed combat photographers to routinely capture most iconic images of many conflicts.
My more detailed post on Buzzfeed that didn't go anywhere (those losers!): http://www.buzzfeed.com/chubachus/the-first-combat-photographs-659n

Fort Sumter Photograph Information: http://www2.timesdispatch.com/news/civil-war/2012/jun/02/first-combat-photos-of-civil-war-are-in-richmond-ar-1959987/

Morris Island Photograph Information: http://www.flickr.com/photos/cwpt/2668079018/

Boer War Photograph Information: http://www.angloboerwarmuseum.com/Boer70z1_hero28_mason.html