Darkmoon Rabbit can't be redeemed through tokens, it's only a drop.
The dropped version is the purple one, reflecting the items rarity (quite hard to get).
Once you learn it and cage it again it will show as blue (rare), as this is the highest quality of pets you can get at the moment.
As far as I know only the breed can differ. You can see the breed on the blue ones, but not on the purple ones, as they haven't been learned yet.
Therefore, if you want a certain breed, get a blue one. If you don't care, just get the cheapest one you can find (purple or blue).