Boosted Elemental Shaman Question

[SirWarrier1 0]

So I decided to use my Legion boost on a brand new level 1 shiny Elemental Shaman. Obviously, learning a new class takes a while, but I'm pretty quick on the draw and after reviewing each spell, testing combinations on training targets and reviewing the info on Icy Veins, I feel pretty competant.

WoD PVE mobs are cake, but I decided to take my new max level to ICC 25H in an attempt for a drop at Invicible. I had absolutely no problems whatsoever until the actual battle with the Lich King himself. Sure, my toon is boosted with booster gear, nothing crazy, but seeing as how I've taken him down with toons of similar ilvl, I didn't think there'd be an issue. As you can imagine, my DPS against him was slow, but it was manageable, I get him to phase three and then I die from Infest. I haven't died from LK since max Cataclysm (other than that blasted Shadow trap when I'm not paying attention). Thinking death was a fluke, I resolved to take him on again. Death. Death, death, death, success.

Now I'm wondering as to the competency of my toon. I'm still confident on my rotation and in playing her as a whole, but that fight has me doubting.
 

I prefer to PvE, and solo at that (She won't be raiding, she'd mostly be running older raids in hopes of rare mount drops), so I'm wondering if Enhancement is a better spec for my goals? Upon trying to get an answer as to which does more DPS, I get the answer that they're roughly the same and to play which is most fun. I'm awesome at all of my max level toons (Most are DPS) but I don't have too many caster-type classes and I'm having a lot of fun with Elemental. But in reality, a fun spec is useless if it can't achieve the purpose it exists for.

Here's my Armory data:
http://us.battle.net/wow/en/character/shadow-council/Ellabela/simple

So the question I'm trying to have answered is: Am I just playing her wrong possibly? Is she just undergeared? Or would it be better to repect to Enchancement for my purposes?