If the characters keep referring to "chickendragons" and "penguindragons" and so on, I suspect you lose the "but these are dragons" wonderment because the reader is going to be expecting them to behave just like chickens and penguins and so on.

If you're going to take it in this direction, I'd go with Stephen Jay Gould's idea that evolution is contingent. Drop dragons into the ecology 65 million years ago instead of theropod dinosaurs, and they'll fill slightly different niches, and even the ones that were in very similar niches would look different. And warm-blooded dragons might not evolve to fit into the penguin niche; there might be more mammals there instead. Take out birds and maybe more marsupials hang on. Hummingbirds are weird and exist only in the Americas; if there were no birds, you might get more bats, or dragons, drinking nectar and pollinating things, but probably not small, bright-colored, hovering vertebrates.

I suspect that your displaced characters wouldn't be saying "chickendragon" and "hawkdragon," unless they're ornithologists: they might start with that, but pretty soon it would just be "hawk" and "chicken," especially if the thing in something like the chicken/jungle fowl niche was worth eating.