When Ursula K. LeGuin's novel "The Lathe Of Heaven" was adapted for PBS, the alien race that was created by George Orr's dreams resembled huge tortoises which stood erect. (I can't remember how they were described in the book, and I can't remember if they even showed up in the TV movie remake starring James Caan - which took a lot of liberties with the story.)
Not that it matters, because that original adaptation from 1980, starring Bruce Davison and Kevin Conway, is the only version that has any bearing in Earth Prime-Time. (If the book ever got mentioned on TV, than LeGuin would be credited with documenting an historical event.)
When George Orr created those aliens out of whole cloth from his dreams, they seemed to exist only so far as to be Earth's invaders (which united the world's previously antagonistic nations into one world body.) There was no mention of their past history, their homeworld, or how well known were they in the cosmos.
But they could have brought into existence with an extensive backstory which would have caused a massive reboot to the universal timeline.
Would the Doctor have been able to detect the two different timelines? And how far back into the Doctor's life did the aliens' existence go?
Based on this picture, maybe their existence reached back at least as far as the Third Doctor.
I have no clue why Jon Pertwee was kissing a turtle, nor do I know if this was part of an established storyline. If so, then it's already locked into the Toobworld Dynamic and thus unavailable for a fanfic crossover with "The Lathe Of Heaven".
But if it's free from any previous televised story, than maybe the Third Doctor was baby-sitting with one of the children of that species......