Well, ok, technically this is a creature write-up, not a character profile, but that's nit-picking. Uni is as much a part of the party as any henchman a PC might bring along on an adventure.
Uni the Unicorn
Unicorn Filly, Lawful
Armor Class: 4
Hit Dice: 3 (21 HP)
Attacks: 1 Horn Gore
Save As: Fighter 7 (9)
Uni was found, separated from her mother, shortly after the heroes came to Mystara. Unable to find the young unicorn's herd, they encouraged her to tag along with them for safety, and she quickly formed a strong bond to the only other true "kid" in the gang, Bobby (her attachment to another child-like creature has temporarily overcome her natural aversion to male humanoids).
Being rather young still, Uni has not developed her species' teleport ability, and her combat skills (AC, To Hit and Damage rolls) are inferior to those of an adult Unicorn. She fluently understands the spoken common and elven languages, but being an animal, even a magical one, is incapable of speaking either one without magical assistance (a speak with animals spell, for example). Uni does, however, share a minor empathic bond with Bobby. While not as strong as such a bond between an adult Unicorn and a human or elven maiden might be, it allows for the two to share very basic communications and ideas. The two are very attached to each other, and Uni's effective morale is 9 when Bobby is within 20 feet of her.
Anyone harming or killing Uni will instantly draw the enmity of her remaining companions, especially Bobby (and the Dungeon Master, who will indirectly aid them in avenging their comrade).