I've been questing and exploring on my dwarf shaman, so far I've done Dun Murough, Loch Modan, and Wetlands. I've also completed the following dungeons - Wailing Caverns, Blackfathom Depths, The Stockade, Scarlet Monastry - Graveyard, Gnomergan & Deadmines. In the days since the Shattering, between questing and dungeon runs, I've reached level 29 without using any Heirloom gear. Leveling speed is a lot faster and smoother with the quest hubs and each hub linking to the next.
One hint for the dungeon quests, if the quest givers don't move forward with you. Teleport out and back into the dungeon, and you'll be back at the beginning with the quest givers.
Quest gear and dungeon drops are generally better than most of the random items drops and will generally have an option that will match you spec, so you'll be ready for for most encounters.
I'm really enjoying working on my shaman. I've decided to level as enhancement, and the melee style is enjoyable. Now that i know Nova blast, I'm having to work in dropping at least a fire totem when facing a group of mobs.
Have fun, and explore the world.