Dove is Puck's horse and her "best friend" (1.5). She may be peaceful compared to the capaill (could that be where the name Dove comes from?) but she's no My Little Pony. Puck and Dove don't sit around and brush each other's hair—they train as hard as the men do, and that training leads them to a victory in the end.
As a character, we don't learn much about Dove. She's a horse, obviously, and she doesn't die, so that's good. Also, Puck describes Dove as "moody and she's slippery and she's in love with the ocean" (26.31). Just as Sean and Corr have a lot in common, we think you could say the same about Puck and Dove.