I just made it to the forth level with my Paladin character, it only took an hour and half or so. I was told that you make it through the first ten levels very quickly, then it starts getting harder.
Note: There are "!" (exclamation marks) at the bottom of the screen to tell you what to do, or why something is happening. Until you're comfortable with the dynamics of the WOW world, I would heed the information.