The Egg of Coot is from module DA1,
Adventures in Blackmoor. It was originally something from Dave Arneson's campaign; Blackmoor was incorporated into the Flanaess, pretty much in name only, and the Egg of Coot has much more recently come along for the ride. I think Fred Weining is to blame, but don't quote me on that. Blackmoor also became part of the distant past of the Mystara campaign, and was released as its own campaign setting in the last year (by Goodman Games, I believe) so there are a lot of different incarnations at work. What the Egg of Coot was/is in Dave Arneson's Blackmoor isn't necessarily what it is in Mystara's Blackmoor or Oerth's Blackmoor.
Another hint of all the different incarnations Blackmoor has had can be seen in Andre Norton's novel
Quag Keep that she wrote after extensive consultation with Gary Gygax. In that book, Blackmoor is conflated with the Great Kingdom.
Dave Arneson and David Ritchie said:
To the north was an evil and unnatural superbeing that called itself the Egg of Coot...
...In his Great Nest north of Blackmoor, the evil Egg of Coot counted his losses at the hands of Blackmoor's army, and he too decided that he hated the new king with a special hate...
...To the northwest of Blackmoor and separated from it by a narrow channel called the Breakers, is an isolated peninsula that rose from the depths so recently that there are men who remember when that barren, stinking tongue of land was open sea. This magically created peninsula is the dominion of an evil and vastly powerful entity that calls itself the Egg of Coot. Few have ever seen the Egg. Those who have seem unable to remember anything about it. But over decades, it has drawn men to its lair and bound them to its evil will. Now, from its capital, the Egg's Nest, it rules a small empire of 20,000 subjects, a quarter of whom are slaves...
...Most of the coastline surrounding the Egg's realm is either rocky cliff or nearly impassible fen... In the north, the spit of land connecting it with the mainland is guarded by a castle called Trollgate, which is manned by 400 soldiers. On the east coast, Castle Ohmafet, with its garrison of 600, blocks the one good landing site. On the south coast, the walled town of Harbol (pop. 3000) controls access to the beaches at the head of Blinkdog Bay. At the head of Coot's Bay is the Egg's Nest, a walled town and port of 6000, inside of which is the Egg's citadel.
Someone who has the other adventures in the DA series (which presumedly stands for Dave Arneson) might know more.
Just as a suggestion, it might be an illithid elder brain pool, perhaps one that's lost the illithids who formally cared for it. Or an elder beholder, for that matter. Both are roughly egg-shaped and powerful. It could also be a sentient artifact. Or maybe it's a literal egg of some cosmic entity - what might happen if it hatched?
Qullans are from the original Fiend Folio, and White Dwarf Magazine before that. They're humanoids infused with chaos.
Here is a conversion to 3rd edition D&D.
The town and castle of Blackmoor in DA1 was suffused with wild magic due to the mysterious black rock upon which it was built, and caused the dungeons beneath the castle to spew up weird monsters on a periodical basis. This explains qullans nicely. You might conceivably consider the black rock to the the basis for a far realm cyst as described in Dragon Magazine #330. Maybe that's what the Egg is after.
See also
Robilar Remembers: Journey to the City of the Gods for details of the original campaign. It's safe to assume it was originally intended to be the same as the one from Dave Arneson's campaign that inspired the
module co-written by Dave Arneson; since Mordenkainen and Robilar adventured in it, that explains how it also ended up on Oerth.
