One character I see cropping up from time to time on lists of favorites is literally a living fossil. Terrybubble is, in fact, a fossilized dinosaur skeleton, with the bones fused together and animated by a geyser in Yellowstone National Park. He ended up on Umbrella Island in the company of Speedy, a scientist's nephew from Long Island who had been to Oz once before, in The Yellow Knight of Oz. He tries to be a pet for Speedy, and is basically a huge skeletal creature that acts like a dog. (Hey, maybe he's sort of the prototype for Dino from The Flintstones, although Terrybubble can talk.) His odd name comes from Speedy's attempt to say "terrible" after being shot into the air by the geyser.
It's not entirely clear what kind of dinosaur Terrybubble is supposed to be, and it's likely that Thompson didn't have any particular type in mind. He walks on his hind legs, but also has a long neck and fairly long arms. One actual species is mentioned in the text, however, and that's a megalosaurus, which ended Terrybubble's first life. The dinosaur says that their name for the predatory species was "mogerith" (or "mogger" for short), and that his home was the Valley of Virtula, perhaps located in or near modern Yellowstone. By his own admission, he was 400 years old when he died. One of his favorite activities is dythrambing, which involves bouncing around and spinning on his tail. I've heard that some scientists believe large dinosaurs weren't as slow and cumbersome as their size suggests, so perhaps Thompson was ahead of her time in making her own dinosaur creation so acrobatic.
It's interesting that, while dinosaurs have been considered cool by children for some time (I was certainly of that opinion in my own youth), Speedy initially comes across as quite bored at the prospect of seeing dinosaur bones. The book was published in 1934, and I suppose by this point dinosaurs were well enough known that Thompson could expect child readers to recognize one, but perhaps not as popular as they later would be.