Using Dog Soldiers
Against other melee units, the Dog Soldier can be considered to have a strength of 8, rather than the Axeman's 7.5. Therefore, it's even more effective for repelling swordsmen, and is an even match against Praetorians.
The Dog Soldier is also very effective for early-game rushes. With no need to spend time building a Copper Mine for resources, a quick army can be formed to conquer opponents who may not have even reached Archery. Try promoting them in Woodsman promotions, so they can get to enemies quickly.
Against Dog Soldiers
As such an effective rushing unit, if you see the Native Americans near you, it may be best to rush to Archery before anything else (other than maybe Religion.) Dog Soldiers are weaker against Archers than normal Axemen, and even more prone to Chariots.
The Dog Soldiers were the elite of the Cheyenne warriors and some of the most feared fighters in the American West. Members of a prestigious fraternal society, the Dog Soldiers each received a "Dog Sash" upon entrance into the group. While at first merely emblems of membership, the "Dog Sash" soon became a symbol of iron will in combat. This reputation stemmed from the Dog Soldier habit of, during particularly brutal combat, staking themselves to the ground by way of their "Dog Sash" and not moving from the spot until victory or death had overtaken them.