I did not write this guide, full credits go to Etermity3632

Okay First: this is the Alliance quest chain for the key to Scholomance. Second: The lvl requirements are as listed on the net, so dont cry if you cant do solo them at this lvl or brag cause you could early. Third: This info is from various sites on the net, if you have info that counters this pls post it so that people are informed. Thanks.
That being said the quest chain is as follows:

A Call to Arms: The Plaguelands – Obtained from any of the criers in IF, SW, or Darn. This quest will take you to Chillwind Camp in Western Plaguelands and have you speak to Commander Ashlam Valorfist. (lvl 50 quest obtained at lvl 50)

Clear The Way – Chillwind Camp, Western Plaguelands
Starting NPC: Commander Ashlam Valorfist. This quest will have you Kill 10 Skeletal Flayers and 10 Slavering Ghouls in Sorrow Hill. Sorrow Hill is a graveyard just northeast of Chillwind Camp. Proceed there and kill the required number of ghouls and skellies and return to Commander Valorfist for your reward. (lvl 52/ obtained lvl 50)

All Along the Watchtowers – Chillwind Camp, Western Plaguelands Starting NPC: Commander Ashlam Valorfist. Using the Beacon Torch, mark each tower in Andorhal; you will need to stand in the doorway of the tower to successfully mark it. Commander Valorfist will provide you with the beacon torch to light the doorways with. Proceed to Andorhal, a ghost town northwest of Chillwind Camp and find the four towers. *NOTE* Unless the gods of warcraft love you there will be an elite of mid to high lvl 50s standing in each tower and you will aggro them when you get close enough. What I did was had a hunter run in freeze trap him while I put the beacon in the doorway, then ran. This was much faster than fighting the 4 elites + all the mobs you encounter in the town. (tower coord: 40,71/42,66/44,63/46,69) (lvl 56/obtained lvl 50)

Scholomance – Chillwind Point, Western Plaguelands
Starting NPC: Commander Ashlam Valorfist. This quest can be obtained at level 55 so you may not be able to get it immediately upon completing the level 50 pre-requisite quest. All it requires is for you to speak to Alchemist Arbington, who is standing a few feet away from the quest giver. (lvl 55/ obtained lvl 55)

Skeletal Fragments – Chillwind Point, Western Plaguelands. Starting NPC: Alchemist Arbington. Kill undead skellies around Andorhal and Sorrow Hill and loot them for the Skeletal Fragments. Once you’ve gathered 15 of those, return to the quest giver for your XP reward and the quest continuation. (lvl 57/ obtained lvl 55)

Mold Rhymes With… – Chillwind Point, Western Plaguelands. Starting NPC: Alchemist Arbington. Bring the Imbued Skeletal Fragments and 15 gold coins to Krinkle Goodsteel in Gadgetzan. This is the crap part about getting the key, it will cost you money… and lots of it. Its easy but the 15g part kinda licks. (lvl 57/ obtained lvl 55)

Fire Plume Forged – Gadgetzan, Tanaris
Starting NPC: Krinkle Goodsteel. Take the Skeleton Key Mold and 2 Thorium Bars to the top of Fire Plume Ridge in Un’Goro Crater. Use the Skeleton Key Mold by the lava lake to forge the Unfinished Skeleton Key. Again this involves money as the quest giver doesnt provide you with the thorium bars. Follow Goodsteel’s instructions and take the unfinished key back to Arbington in Chillwind Camp.
(lvl 57/ obtained lvl55)

Araj’s Scarab – Chillwind Camp, Western Plaguelands
Starting NPC: Alchemist Arbington. Destroy Araj the Summoner and bring Araj’s Scarab to Alchemist Arbington at Chillwind Point, Western Plaguelands. Araj’s Location: In the middle of Andorhal. East of the Big Townhall. 45,69, surrounded by a throng of undead. It can be a tough fight because of the sheer number of mobs, and the fact that Araj himself is a (I do believe) 61 elite. Take a friend, or two… or three lol. (lvl 60/ obtained lvl 55)