The "unwritten" rules of English adjective ordering support this RFE - and so do I. Baby <foo> dragon is the way to go.
Additionally, if you consider "red dragon" as a distinct species in its own right, as per ADOM's inspirations and metaphysics, as opposed to a dragon that just happens to be reddish? Then no other descriptors should be placed between those terms.
As for replacing the word "baby" itself, potential options could include "infant", "immature", or even a suffix of "hatchling" ("red dragon hatchling"), but I don't see anything wrong with the original term. "Young" is too vague a descriptor to be useful and yet too specific a piece of information for the PC to be aware of. That is, the PC doesn't know how old the dragon actually is, but they can tell the dragon's approximate life stage by its size and physical traits.