Download the Dungeon Journal addon - this will make collecting all of the dungeon quests MUCH easier.
There is a bit of flexibility in what level you do things, but I like questing straight to 16 and then starting dungeons so I can run a bunch of different ones in a row. After the update, you now get at level 10, so you can do huge threat in dungeons right away.
For each level range mentioned, I'm mainly focusing on dungeon suggestions, since that's probably what you're most interested in as a tank player. But you always have the option to just quest or grind mobs and skip some dungeons or do them at different levels than I list here. There's no set in stone way you have to level; I'm simply giving suggestions.
Level 1-13~: Tirisfal Glades / Durotar / Mulgore / Zephras Isle
Just basic questing with a 2 hander. Some zones have more quests than others, but you'll be somewhere between 12-14 when you do most or all of the quests in your starting zone.
Level 13-16: Silverpine Forest or The Barrens
If you go about halfway into 16 now, you'll be level 20 after running Ragefire Chasm and Ruins of Lordaeron, so you can just go right into Wailing Caverns with
Cleave,
Retaliation, and
Victory Rush.
Level 16-18 Ragefire Chasm
At this point, I like to run all of the dungeons. Download the Dungeon Journal addon to easily see all of the quests for each dungeon and where to get them. In Forever, the vast majority of dungeon exp comes from the quests due to dungeon quest exp buffs and dungeon mob exp nerfs, so you really want to make sure you have every quest for a dungeon before you run it.
Now that you're level 16, you have the very strong
Shield Block +
Revenge, which allows you to guarantee you're able to cast
Revenge every 5 seconds. Combining this with the survivability from
Demoralizing Shout and
Thunder Clap, you can grind mobs easily and pull 3-4 at a time.
Level 18-20 Ruins of Lordaeron
If you aren't quite 18+ yet, you can quest in Silverpine Forest or The Barrens or grind mobs.
Level 20-22 Wailing Caverns
If you aren't quite 20 yet, just do a few quests to get there so you can have all the fun new level 20 abilities for Wailing Caverns. The quests around Camp Taurajo in southern Barrens are great for some quick exp. If you didn't already do the The Forgotten Pools quest chain to unlock the Wailing Caverns quest step, you can just do that.
If you want to skip this dungeon, you can quest in Stonetalon Mountains, Thousand Needles, The Barrens, Ashenvale, or Hillsbrad Foothills.
Level 22-24 Shadowfang Keep
If you aren't quite 22+ or want to skip this dungeon, you can quest in Southern Barrens, Stonetalon Mountains, Ashenvale, or Hillsbrad Foothills or grind.
Inside SFK, grab the Black Tome next to Arugal at the end of the dungeon. You can use this later to summon an extra boss in the City of Dalaran dungeon.
Level 24-26 Blackfathom Deeps
If you aren't quite 24+ yet or want to skip this dungeon, you can quest in Hillsbrad Foothills, Stonetalon Mountains, Ashenvale, or Thousand Needles or grind.
Level 26-28 Quest/Grind
The next dungeon we'll tackle is the new Excavation Site dungeon, but there's a lot of tank damage in there, so I recommend getting to 28 before doing it.
In this level range, you can grind or quest in Hillsbrad Foothills, Thousand Needles, Stonetalon Mountains, or Ashenvale.
Level 28-30 Excavation Site
If you aren't quite 28 or want to skip this dungeon, you can quest in Hillsbrad Foothills, Thousand Needles, Stonetalon Mountains, or Ashenvale or grind mobs.
The quest from the Titan Relic will send you to a new area in Northern Mulgore. This spot is fanastic for prot war farming, with tons of hyper spawning mobs that you can easily pull 3-4 of. Do the quests while you're here and stay a bit to grind if it's open to hit 30+.
Level 30-32 Razorfen Kraul
You don't need to be 30 for this, but you probably will be if you made good use of the spider hyper spawn. If you want to skip this dungeon, just keep grinding spiders or quest in Thousand Needles or Hillsbrad Foothills.
Level 32-34 City of Dalaran
You can do this before 32, but you'll probably be 32+ already by this point. If you want to skip this dungeon, you can quest in Shimmering Flats (Thousand Needles), Arathi Highlands, Stranglethorn Vale, or Alterac Mountains (Hillsbrad quests) or grind.
Level 34-36 Gnomeregan
You don't need to be 34 for this, but you probably will be if you've mostly been following this guide. Gnomer does only have one Horde quest, so it isn't the best exp reward for your time. If you want to skip it, just grind or quest in Arathi Highlands, Shimmering Flats (Thousand Needles), Stranglethorn Vale, or Desolace.
Level 36-38 Quest/Grind
Grind or quest in Stranglethorn Vale, Desolace, Arathi Highlands, Riverglades, Swamp of Sorrows, or Badlands.
Level 38-40 Riverglades Questing
Can also do SM
Level 40-42 Razorfen Downs / Drowned City
If you aren't quite 40+ or want to skip this dungeon, you can grind or quest in Stranglethorn Vale, Riverglades, Swamp of Sorrows, Badlands, Feralas, or Tanaris..
Level 40-42 Razorfen Downs
If you aren't quite 40+ or want to skip this dungeon, you can grind or quest in Stranglethorn Vale, Riverglades, Swamp of Sorrows, Badlands, Feralas, or Tanaris.
Level 42-43 Krol'dok
If you aren't quite 42+ or want to skip this dungeon, you can grind or quest in Stranglethorn Vale, Riverglades, Swamp of Sorrows, Badlands, Feralas, or Tanaris.
Level 43-47 Zul'Farrak and Uldaman
If you aren't quite 43+, you can grind or quest in Feralas, Tanaris, Stranglethorn Vale, Riverglades, Swamp of Sorrows, or Badlands.
Level 47-49 Maraudon
If you aren't quite 47+ or want to skip this dungeon, you can grind or quest in Feralas, Tanaris, Searing Gorge, Azshara, or Felwood.
Level 49-51 Alcaz Prison
If you aren't quite 49+ or want to skip this dungeon, you can grind or quest in Hinterlands, Searing Gorge, Azshara, Felwood, Feralas, or Tanaris.
Level 51-53 Sunken Temple
If you aren't quite 51+ or want to skip this dungeon, you can quest in Hinterlands, Felwood, Un'goro Crater, or Azshara.
Level 53-55 Grind/Quest
If you still have Un'goro Crater questing left, that's the best thing to do at this point; grinding in Un'goro is great too. You can also knockout the Western Plaguelands quests and possibly grind at the farms if they're open.
Level 55-57 Blackrock Depths
At this point, it's best to just start farming endgame gear and not worry about any open world questing or grinding anymore. BRD has tons of quests, early endgame gear, and potential Pre-BIS. If you can't find a group for whatever reason, you can quest in Eastern Plaguelands, Western Plaguelands, Winterspring, or Silithus
Level 57-60 Blackmaw Hold
New endgame dungeon that will have some Pre-BIS gear to start farming.
Level 58-60 Shaper's Terrace, Stratholme, Scholomance, Blackrock Spire, Dire Maul
These are the endgame dungeons that will drop your Pre-BIS gear, so it's good to get started on the grind while you're still leveling.