Thanks to Adam's hint I found a web shop selling these beautiful creatures!
They don't just sell one of them, you will need to buy a whole bunch. Price starts at $6 if 50 of them get ordered.
I'm quite sure that there will be 50 of us wanting such a "Super Soft Stuffed Animal- Unicorn". Even if there is no logo printed on their t-shirts. (Because as I pointed out in a comment on my answer here, unicorns don't need a logo to have a point.)
But I don't know how this could be organized. Of course one of us could buy the lot and then re-sell them, but that means a lot of work, given that many of us live anywhere but in the US. Any ideas?