Dungeon leveling is undoubtedly the best method for leveling any character in WoW. Dungeon leveling is a lot more effective and efficient for leveling characters for a number of different reasons. The most obvious and most beneficial reason is that Dungeons offer much higher XP rewards for completing challenges as Blizzard consider Dungeons to be a lot more difficult than solo questing.
Although this is true to a certain extent, a dungeon player is only as good as the group they're operating with. Dungeons require groups and some team work is involved to complete the dungeons and conquer the bosses whereas solo quests are individuals completing each quest on their own.
Another advantage to dungeon leveling is that you'll spend a lot less time dead and resurrecting your body as you and your group are annihilating the mobs continuously with some of the group members having healing capabilities and some heavy hitters on the front line.
One over looked advantage to dungeon leveling is you hardly spend any time traveling between quests. As you'll know traveling between quests in solo play can be quite tedious and cumbersome. The Dungeon Finder tool will take you right to your instance saving a great deal of time.
Another huge advantage dungeon leveling has over solo questing is the rewards on offer! You'll find that much better loots drop in dungeons which will allow you to equip your player with much better gear and stronger weapons, armor e.t.c
There are a three different ways in which you can obtain these special loots in dungeons. Firstly, each dungeon has its own quests to be completed and it's well worth completing each available dungeon quest for the rewards, both gear and XP.
You'll also drop some awesome loots for killing the dungeon bosses and the elite monsters that can only be found in dungeons.
Finally you can drop some awesome loots from the special bag which is rewarded to you after you have conquered the first random dungeon of the day.
As you can see there are lots of nice loots to be gained in dungeons as well as a lot more XP that can acquired in a lot less time. The only drawback to dungeon leveling is you'll miss some other aspects of the game when solely using this method, although one can catch up on those at a later date once their character is leveled and well equipped.
Dungeons also bring a more engaging and social aspect to the game that can't be matched with solo leveling and is a great way to network and grow your character fast.
All in all dungeon leveling has proven to be a lot more effective for leveling than solo quests and should definitely be considered. You'll also want to plan your class leveling build for a good dungeon build for up to level 80.