I love how a Unicorn is the mount for White Mage. I love how the tanks get unique mounts through tanking in duty.

I wish the other jobs had unique mounts, so here are some ideas I have.

Healers

Ast: A floating crystal ball with a constellation inside.

Scholar: Fairy wings

New tank

Gunbreaker: Something magitek, or VII themed.

DPS

Black Mage: Something Mach themed.

Summoner: Probably some kind of summon mount similar to Carbuncle mounts. Maybe it could be a ruby carbuncle, or demi Bahamut as a mount.

Samurai: A mechanical automation, or a samurai armored horse.

Machinist: Something Magitek

Blue Mage: Obviously a random monster.

Red Mage: A horse in an elegant outfit.

Bard: Probably some kind of musical themed animal. Maybe a bird that makes a singing noise when mounted.

Ninja: A Japanese automation.

Dragoon: A unique dragon

Monk: Probably an armored Griffin

Those are just my ideas~