I realize a lvl 65 might not seem like a new player but I still consider myself new. This is my first WoW character. So Basically I'm wondering if it's worth it to complete all the quests in the outlands? I could just keep doing dungeons to level up faster and the gear in dungeons seems to be better than what I'm earning by questing. So my question is am I missing out on anything important by not doing quests in the outlands, northrend etc..?

As others have mentioned, you certainly have a wide variety of options available to you in order to progress steadily toward 85, but both dungeons and questing offer some unique and valuable experiences in their own right. So it really might be in your best interest to do a bit of both. Some quest chains even lead you towards running a particular dungeon for especially appealing rewards.

Since you are a Protection paladin, running dungeons will also give you some valuable tanking experience that will be incredibly useful to you all the way to 85 and beyond. As you noted: you can also receive gear and weapons from dungeons, which can be a great asset to you while leveling. Questing, on the other hand, offers unique rewards including not only gear upgrades, but a lot of fun and unique items like the X-52 Rocket Helmet.

Don’t forget that there are loads of items that you can pick up along the way for Transmogrification purposes, too. Regardless of whether or not they are an actual upgrade for you, if you groove with how they look, you should make sure to snag them up so you can Transmogrify them later. In most cases you won’t be able to obtain them any other way outside of Outland’s unique dungeons, drops, and quests.

In addition, if you haven’t experienced the multitude of stories that are taking place in Outland, I feel like you would be missing out on a lot of really great stuff if you skip it entirely. That’s not to say you should feel compelled to finish every single quest you can find (there are achievements for that sort of thing, after all!), but you might enjoy at least doing a handful of quests in each zone in order to get a feel for all that’s taking place during The Burning Crusade. In many cases, for me, I actually found that once I’d taken a few steps into a particular quest chain, I ended up really wanting to find out how it ended, too.

In addition to a lot of heavily lore-driven quests, there are also some downright amusing ones, such as one that involves tossing a Booterang at some particularly lazy peons. And who would want to miss out on slinging a booterang? ;)