I've never seen an original manuscript of the book, but I came across a nice video on the website of the Bibliotheque nationale de France that shows one up close. In the video, the host offers some interesting background information on the book, and even if you can't understand a word she says (it is all in French), it is still a cool video to watch since you get a sense of the size and thickness of the book and the richness of its illustrations and text.
In the time of Gaston Phébus, there were no breeds of dogs, just general types. The dogs in this image were called 'chiens d'oysels' ('dogs that serve the bird' ie: a hawk or falcon). Illustration from Le livre de la chasse.