And make use of your hearthstone in a strategic manner.

Draenei area has a lot of clustered quests up until level 5. There are a few collection quests, though -- the flower collecting one and the shuttle parts by the moonkins come to mind, and if there are too many draenei you'll have to wait for respawns. When I level 5 in the draenei starting area I always have to wait a bit for a respawn of the shuttle parts.

I'd agree on the rogue thing. Maybe even a warrior, but thanks to rage their power is backloaded, whereas a rogue's is frontloaded. Stay away from hunters under level 10. Casters mana might be an issue depending on how much you push them. Warlock could work if you make good use of the pet. But Rogue sounds best for leveling 1-10.