I've seen baby buns, depending on the breeding they do look like this.

I've also seen fairly realistic stuffed animals made by that company that does that, I forget the name. So it could go either way.

This could be a stuffed toy, it would still be real.

You can search goggle: images dwarf rabbit, and one very similar comes up. This is not mine but apparently they get up to about 1 kg max. My wife got this from *girls' channel*, a Japanese site. There, it was also controversial, but got a pass from "rabbit experts." In Japan, the price would be ~ $300 to about ~$700, but you have to be careful since some people sell them as dwarves  
but they get much bigger. Caveat emptier

So now I want one that's 6'+ at the shoulder and capable of carrying me on its back

Really real