Spec-wise, you should certainly consider speccing into Test of Faith and Empowered Renew. Speccing into Renew gives you a lot of versatility. At the very least, I'd recommend getting 1/3 Empowered Renew so that you can crit with it (and thus get Holy Conc and SoL procs). Test of Faith gives you a powerful throughput boost when it's really needed. I would take some points out of Empowered Healing, which is a decent but not crucial talent.
You also should drop either your FH or PoH glyph for Guardian Spirit. While it won't help you succeed on the meters, having that cooldown every minute is extremely powerful.
I think you made the right call with your weapon, at least until you can get the offhand from H HoR (if you have the patience and time, farm it every day).
Your gear is otherwise pretty nice. I would definitely use your frost badges to complete your 4 set bonus, as the boost to Circle of Healing is very nice.
I notice one pure spirit gem - spirit is a decent stat but not as strong as intellect for mana regen. I would only use spirit in the form of purple or green gems. Another thing to consider is replacing your boot enchant with Tuskarr's Vitality, the speed boost is nice for any raider.
But really, I only see minor issues with gear and spec. Without some logs or more information on your playstyle, it's hard to tell you where you're going wrong or if you're going wrong at all (it's entirely possible that the meters are inaccurate). Part of the difficulty of a Holy Priest is knowing when to use your different spells - when to use Prayer of Healing, when to use Renew, when to use Flash Heal, etc etc. It takes a lot of practice.