Can someone tell me what I need to do to start the quest involving the Morag Tong? Also, do I need to be considered the Dragonborn to do this quest?

The Morag Tong is part of one of the quests started at Raven Rock. And no, you don't need to be the DB to do it.

I wish the Morag Tong had a questline missed opportunity Bethesda!!!

Agreed, though it has been pointed out that it would be difficult to do considering some players are already in with the Dark Brotherhood.

Ahh. Yes i could see a discrepancy in there somewhere ..

So how do we get the Morag Tong quest? I would also like to know.

Also, someone in skyrim mentions that the morag tong disbanded after the eruption, suggesting the group you kill were possibly the last remaining members

You get it from the Councillor's steward - regarding an assassination attempt. I can't remember the quest or the guys name - they are all too new

It's the dark elf that joins the thrives guild somewhat late into the quest line.

Also, I can say firsthand that if you are in the Dark Brotherhood, people will put out hits on you because if it. One of the notes I got off of a Morag Tong that attacked me said they were sent to kill an associate of the 'dishonorable assassins.' Or something to that effect.

Yeah you do, you have to be recognized as DB to even start the DLC*.

No you don't. To start the MQ you need to be DB but to visit the island or do the side/misc quests.

actually both are right in a way lol
first you have to start a quest named Marched of dead complete that and you can start a quest called the served cold and bam you will get your morag tong in that quest
now tell me im pretty

Also if you just gotten to reven rock and just want the morag tong out fit then you have to do the mine quest as well if not it wont show up

So basicly do the marched for dead and the final descent if you have just gotten to raven rock