It's a unicorn. Yep, Scotland's national animal isn't even real. Let's not be negative-nellies here, the unicorn looks damn fine on a crest, and this fiction animal as the symbol of Scotland is just as legitimate as a lion being the national animal of England. England is so known for their lions.
Just browsing through the list of national animals on Wikipedia, I'm happy to say that Scotland isn't the only country to use a fictional animal. In fact, Scotland isn't the only country to use a fictional horse! Enter North Korea with the Chollima. The Chollima is the East Asian equivalent to Pegasus. The winged horse was originally a Chinese fabrication, but became North Korea's national animal during reconstruction after the Korean War. I'm not interested in giving too many compliments to the extremely oppressive dictatorship, but they picked a great national animal and they've turned it into an amazing statue.
Most countries with fictional creatures as national animals have had long histories with them. Dragons and birds seem to be the most common. A few European countries like Serbia and Russia have emblems with two-headed birds. China and Wales both use their own versions of the dragon. Meanwhile, Greece chose the phoenix.
These are terribly limited fantasy creatures: birds, horses, dragons. Sure they're steeped in culture and tradition, but I wish at least one country would have picked something outside the box. One could use a hydra, cockatrice, or tarasque as their symbol... I know, those are just more dragons and birds... Well, how about Shoggoth, an amorphous horror from H. P. Lovecraft's At the Mountains of Madness:
"It was a terrible, indescribable thing vaster than any subway train—a shapeless congeries of protoplasmic bubbles, faintly self-luminous, and with myriads of temporary eyes forming and un-forming as pustules of greenish light all over the tunnel-filling front that bore down upon us, crushing the frantic penguins and slithering over the glistening floor that it and its kind had swept so evilly free of all litter."
I think this would be a terrific national animal for Antarctica.