2-D universe

An inter-incarnational sequence of adventures stretched from the Fourth Doctor's encounter with the Iron Legion to the Eighth Doctor's travels with Destrii, (COMIC: Doctor Who and the Iron Legion, The Tides of Time, The Shape Shifter, A Cold Day in Hell!, Endgame, The Fallen, etc.) sharing a continuous reality with various standalone adventures of early Doctors, (COMIC: A Life of Matter and Death, Ground Zero, etc.) the lives of aliens around them, (COMIC: A Ship Called Sudden Death, The Company of Thieves, etc.) and further adventures continuing into the Ninth Doctor's life and beyond. (COMIC: Art Attack, Thinktwice, The Stockbridge Showdown, etc.)

While the majority of sources indicated this reality to be the same as the Doctor's universe as a whole, (PROSE: Deceit, The Scarlet Empress, Prime Time, AUDIO: No Place Like Home, TV: Time Heist, The Doctor Falls, COMIC: Vortex Butterflies, etc.) some, focused on the Sixth to Eighth Doctors, indicated it to be its own reality separate from other strands of the Doctor's life. (AUDIO: Zagreus, Signs and Wonders, PROSE: Spiral Scratch, The Eighth Doctor Part 2, At Childhood's End) The Eighth Doctor of another world was also seen to dream of his adventures in this universe. (COMIC: The Land of Happy Endings)

Fate
By the end of the Eighth Doctor's life, by one account, this strand of reality reconnected with the parallel histories where the Eighth Doctor had travelled with Sam and the Eighth Doctor had travelled with Charley, such that from the perspective of the Last Great Time War and beyond they were all in the Doctor's past. (PROSE: The Eighth Doctor Part 2)

Among the palimpsest universes before the Infinity Doctor's reality, Omega had seen a universe where Rassilon ruled Gallifrey from the Matrix, (PROSE: The Infinity Doctors) as was the case in his role as Matrix Lord throughout this sequence of events from the Fifth Doctor's life to the Eighth's. (COMIC: The Tides of Time, The Final Chapter)

Relation to other realities
During his multiversal adventure, the Sixth Doctor saw a version of himself who travelled with Frobisher. (PROSE: Spiral Scratch)

When Ace was shown her future, she saw "several universes" of possibilities, including one where she was surrounded by giant fleas. (AUDIO: Signs and Wonders) When exposed to anti-time, the Eighth Doctor of the positive-time universe saw himself "on the planet Oblivion facing a race called the Horde". (AUDIO: Zagreus)

By one account, whilst travelling with the Seventh Doctor, Ace was shown multiple possible futures in her timeline by a Quantum Anvil, which included her death in a Nitro-9 explosion. This incident led her to leave the Doctor. (PROSE: At Childhood's End, COMIC: Ground Zero)

The detonation of Qqaba which destroyed the original palimpsest universe bore a great resemblance to (PROSE: The Infinity Doctors) the account of the soon-to-be-Matrix-Lord Rassilon's detonation of Qqaba. (COMIC: Star Death)

The Eighth Doctor of this reality also dreamed of another world featuring a copy of himself haunted by less angst. However, this relationship seemed to go both-ways, as the Doctor's more innocent counterpart also seemed to dream of the angst-filled world. (COMIC: The Land of Happy Endings)

Behind the scenes

 * Early Big Finish Productions stories featuring Frobisher were branded as Side Steps into "a 2-D universe".

Information from invalid sources
Ken Book interviewed Beep the Meep for Doctor Who Magazine, and after Ken asked if Beep had any plans to appear on television, he responded no, explaining it was a "backwards step" that'd be repeating what had already been done thirty years prior in The Star Beast, and ultimately, he didn't consider Doctor Who on TV to be canonical. He also added he was afraid they'd "do [him] in CGI". (NOTVALID: Who on Earth is... Beep the Meep)

The Land of Happy Endings
Despite common fan readings of the story, the intention of COMIC: The Land of Happy Endings was that both worlds seen in the story were entirely valid realities. Because of this, while one could say that John and Gillian's world was a dream, the exact same claim could be made about the DWM reality.