Being an Actual Dragon
The LA and Racial Hit Dice rules made by WotC are really really bad. No-one should ever use them. They are literally insane. You have to be like level 50 or something to play the sort of dragon that shows up as an enemy at level 15.
A much saner approach is the CR system. A level 15 PC is supposed to be CR 15. With a few exceptions, a CR 15 monster is the same as a level 15 PC. You should always run this past your GM/local optimizer, but usually it's utterly fine. Find a dragon with an appropriate CR (same as group's level, or lower) and then play it. Change out the feats or whatnot. Then advance via normal levels (gain a level when party does), or advance via CR ('bank' levels until you can advance an Age Category of your dragon type, when the party's level is enough to be that CR). Totally not broken. Will not break the game. Is fine. Much less powerful than a Wizard of the same level.
There is no way to be a level appropriate dragon otherwise. Not by RAW.
'Sorta' a Dragon
Shapechange is a spell, Sorc/Wiz/Druid 9, that lets you turn into a creature with HD = your level and you gain supernatural abilities (like Breath Weapon). It has a duration of 10 minutes/level, and can be extended (through a Rod), so at level 17 when you get the spell, it can last for 340 minutes, or, 5 hours and 40 minutes. With enough spell slots, it can be up all day. Similarly, Polymorph and Draconic Polymorph can get you lesser dragon forms.
A more efficacious method, however, is the Psionic Sandwich Trick. Except instead of a sandwich, find and subdue an appropriate Dragon, render it unconscious, and do Sandwich things to it. With the Astral Seed approach, you ARE that Dragon now - it's not dispellable, or disjoinable, or an enchantment of any kind - you are forever, and permanently, that dragon. And also a Psion.
Very Dark Sun-ey.
Druids get Dragon Wildshape through shenanigans, you can be a dragonborn, you can get a (crappy) dragon mount, but your only real options are pretty much the above, for being a genuine, 'giant freakin' dragon' dragon.
Dragonfire Adept until you get Tiamat Breath. Dip Incarnate or take the Open Lesser Chakra feat, grab Spellward Shirt Soulmeld. With Expanded Essentia feat, bonus Essentia feat and Incarnate's level 3 class ability, and being at least level 15, you can put 5 essentia in there, which is SR 29. With Daazzix's vest, that's SR 34, or decent SR. Be a Half-Ogre or Half-Minotaur for size. Get the Feathered Wings Graft, and some more Grafts that give natural armour bonuses. Dip Totemist or burn another feat and grab Wormtail Belt Soulmeld. Should give in the realm of +10ish Natural Armour with the grafts and soulmeld. Be either Feral to get more Natural Armour and claws, or have gone Totemist and bind something that gives claws (Landshark Boots is a good choice) to your Totem chakra. So, you have Size, Natural Armour, Spell Resistance, Claws, Breath Weapon, Flight, and Invocations from dragonfire adept that hopefully are 'spells' enough for you.
Ta-da! I call it a 'make your own dragon' dragon.