Unfortunately the Dragoon isn't gonna have Jump. It sucks, but there is nothing I can do. If you simply can't live without a Jumping Dragoon, then I'd suggest making Cid your dragoon so that you can use his limit breaks, which include Boost Jump.
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EDIT:
Black Mage Abilities: Fire, Ice, Bolt, Fire2, Ice2, Bolt2, Fire, Ice3, Bolt 3, Drain, Freeze,
Break, Tornado, Flare, Ultima, (Kjata?)
White Mage Abilities: Cure, Esuna, Barrier, Mbarrier, Life, Holy Ray, Regen, Cure 3, Drain, Wall,
Death, Full Cure, Holy Flash, (Phoenix?)
Time Mage Abilities: Sleepel, Silence, Confu, Berserk, Haste, Slow, Drain, Comet,
Mad Frog, Death, Bioshock, Silentshrink, Comet2, (Hades?)
Summoner Abilities: Choco/Mog, Shiva, Ifrit, Rumah, Titan, Odin, Leviathan, Bahamut,
Kjata, Alexander, Phoenix, Neo Bahamut, Typhoon, Hades, Bahamut Zero, Knights of Round
Blue Mage Abilities: Enemy Skills (many yet to be determined)
Samurai Abilities: Bioshock, Earthenbonds, Deadly Slumber, Silent Riddle, Confu, (Titan?)
Dragoon Abilities: Reis’s Wind, Lancer, Dragon Force, Dragon’s Gale, Mbarrier, (Bahamut?)
Ninja Abilities: Tsunami, Tropic Wind, Lucky Strike, Fire2?, (Ifrit?), (Leviathan?)
Berserker Abilities: Mad Rush, Explode, Last Stand, Berserk
Knight Abilities: Ice Punch, Thunderslash, Stock Breath, Barrier
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Universal Materia:
Spirit Plus, HP Plus, Speed Plus, Magic Plus, Luck Plus, Chocobo Lure, Mega-All, Underwater,
HP<=>MP, Long Range, Sense, W-Magic, W-Summon, W-Item, All, Magic Counter, Elemental,
Quadra Magic?
EXP Plus: Blue Mage
Gil Plus: Samurai
Enemy Away: Blue Mage
Enemy Lure: Berserker, Knight
Pre-Emptive: Ninja
Counter Attack: Samurai, Dragoon, Ninja, Berserker, Knight
Cover: Knight, Berserker, Samurai
Counter: Samurai, Dragoon, Ninja, Berserker, Knight
MP Turbo: Black Mage, White Mage, Time Mage, Summoner
Booster: Samurai, Dragoon, Ninja, Berserker, Knight
MP Absorb: Black Mage, White Mage, Time Mage, Summoner, Dragoon
HP Absorb: White Mage, Dragoon, Knight
Added Effect: Time Mage, Samurai
Sneak Attack: Ninja, Berserker
Final Attack: Samurai, Dragoon, White Mage
Added Cut: Samurai, Ninja, Dragoon, Berserker, Knight
Steal as Well: Ninja
Morph: Blue Mage
Deathblow: Knight, Berserker
Manipulate: Blue Mage
Mime: Mime
Enemy Skill: Blue Mage
2x-Cut: Samurai, Dragoon, Ninja, Berserker, Knight
4x-Cut: Samurai, Dragoon, Ninja, Berserker, Knight
Throw: Ninja
Coin: Samurai
Steal: Ninja
Mug: Ninja
Slash-All: Samurai, Dragoon, Ninja, Berserker, Knight
Flash: Samurai, Dragoon, Ninja, Berserker, Knight
Of course this isn't set in stone. I was trying to keep classes as pure as I could, but I soon found that given the number of abilities that I sacrificed, some classes were at significant disadvantages. So, I had to open up some materia and abilities to more classes than I originally intended. I can justify allowing all classes to use Quadra, W-, and 4x, since these will all appear near the end of the game, and every character needs to be able to have a way to cause at least 9999 damage. The Blue Mage might not have this option, but has the advantage of a wide variety of skills, most of which are stronger than average for the part of the game you will get them at. You may notice that the Berserker has some abilities. How will he be able to use them? I'll save that for when I start designing the equipment. Also, I am toying with the idea of allowing certain other classes access to a summon or two. Not sure if the benefit outweighs the harm.