Do you mind sharing the armoury of the hunter you're using to solo dungeons?
Dungeons scale to your level and generally are very difficult to solo.
With time and patience i think these would be the best vs Bosses:
T1 - This will work. It may take a while but you'll be able to do it.
Resto Shaman, Prot Paladin, Disc Priest, Mistweaver Monk, Holy Priest, Holy Paladin
T2 - This will be hard. You may run out of mana due to healing yourself.
Moonkin, Elemental Shaman, Guardian Druid, Retri Paladin, Hunter, Warlock, Spriest
T3 - This will be hard. It may be impossible depending on the boss.
Enhance shaman, WW Monk, Fury Warrior, Brewmaster Monk, Feral, Prot Warrior
Not Possible
Arms Warrior
Rogue
Mage