Is Fantastic Beasts and Where to Find Them an exhaustive list of magical animals in the Harry Potter world?

I do think it's particularly telling that Nagini -- the kind of snake she is -- is missing from Fantastic Beasts and Where to Find Them. There are magical snakes listed in FBAWTFT, such as the Ashwinder and the Runespoor. I agree with Gabe in that Nagini is a Muggle snake -- a Naga snake, to be specific (a snake which has mythical properties according to Hindu legend, and most resembles a giant cobra). I find it interesting, though, that Voldemort would choose a Muggle snake for himself. That seems telling in some way, although how I'm not sure.

Anyway, there are creatures missing from FBAWTFT that are mentioned in the novels:

• Hinkypunks
• Blast-ended Skrewts (Hagrid somehow invented these creatures, but one was included in the third task of the Triwizard Tournament, which gives it legitimacy).
• Animagus (this one is iffy, but if a werewolf is listed, I think an Animagus might be worth a mention. However, Animagi turn into Muggle animals, not magical creatures, so it's quite likely this wouldn't apply. Because, really. Being a unicorn Animagus would be so Mary Sue).
• Blood-Sucking Bugbears
• House-elves
• Double-ended newts
• Boggarts
• Owls (Owls in Potterverse have some unique qualities, such as being able to find anyone anywhere and the ability to not be tracked. They also want payment for their services. They're just different than Muggle owls)
• Ghosts, spirits, and poltergeists
• Veela
• Hags
• Giants
• Goblins
• Dementors
• Nargles¹
• Crumple-Horned Snorkack¹
• Unknown Creatures in the Lestranges' vault at Gringotts: [T]he door of the vault melted away to reveal a cave-like opening crammed from floor to ceiling with golden coins and goblets, silver armour, the skins of strange creatures, some with long spines, others with drooping wings[.] (These could obviously be skins of already known creatures which are simply not identified as such)

¹Kidding, kidding ...