I was thinking of doing the same.
I know Horde leveling areas like the back of my hand at this point, so trying alliance might be a fun detour.>>463414821
In classic: not very. Here's the problem that has always existed in Classic, at some point in the 12-15 range, you're going to have to visit three of the most boring zones in the game. The Barrens, Thousand Needles, and the Salt Flats. All three places that almost made me bounce off of WoW.
If you're fine with going to contested areas, you can do half of the barrens, skip the other half, and go straight to strangethorn vale. Come back to do the instance at the end of the barrens after you hit 20 or so.
Trust me, you're gonna want to skip the barrens after five levels in it because it's one of the most annoying leveling areas ever put into a video game. A giant, straight line with no NPCs and no travel points (at least when I played, I hear they added two of them that weren't there before)