So dinosaurs in prehistoric Oz aren't called dinosaurs, of course, because <em>deinos</em> means terrible, and that's not appropriate. These would be, oh, <em>thaumasaurs</em>, "marvellous lizards".
Prehistoric Oz is divided into four regions, one each more-or-less Permian, Jurassic, Cretaceous, and Tertiary in character. It is an island continent, surrounded by ocean -- the deadly deserts are the residue of those dried-up oceans.
The most important new character from the prehistoric time period is the Happy Smilodon (parallel to the Hungry Tiger and Cowardly Lion).
Dorothy sees a giant vertebrae being exposed by a farmer's plow, asks the Wizard about its resemblance to dinosaur bones, he explains (being the all-purpose know-it-all of Oz, but not an asshole like that Wogglebug jerk) about Oz having thaumasaurs instead. Then an accident; Dorothy et al. get catapulted back in time. Ozma's magic picture can't find them, so the wishing belt can't bring them back. Stranded in a magic land that's not a fairyland, they have to find a way home, when they're not even sure there's a way home. Ozian adventure ensues.
Another possible character would be inspired by Dinosaur Comics' Professor Science.