It is actually a very cute animal, trying to eat as much as it can among much bigger "normal" rabbits.
The video was uploaded on Youtube on May 21 by someone who says he/she lives in the area in Fukushima Prefecture close to Fukushima I Nuclear Power Plant.
In one of the replies to the comments, he/she says the location is "500 meters from No.34 in the Ministry of Education's radiation map." No.34 in the radiation map is "Ookawara, Ookuma-machi, Futaba-gun, 7 kilometers from Fukushima I Nuke Plant, south by southwest."
The youtube video has received a ton of negative comments from the Japanese viewers calling it fake and fear-mongering. Reading the comment by the person who uploaded it, I don't get that feeling and the video doesn't look like a fake, but it's just me.
The person who uploaded the video says it is one of their rabbit, and it was born after they fed their rabbits with their favorite fresh green grass after the Reactor 3 blew up. He/she says "We were working in our backyard when the Reactor 3 blew up, which we didn't know at that time. Our faces and throats felt burned, and we thought we're going to die. So we fed the rabbits with their favorite grass." And "It's just too late, telling us after 2 months how contaminated the soil is around here. We've drunk from the well water, have eaten the wild mountain vegetables."
Some samples of viewers' comments (original in Japanese); many of them attacking the messenger (the person who uploaded it):
What a cute little rabbit. Breed as a new breed.
There's no proof that this video was shot in Japan!
That cannot be in Fukushima. Dubious video.
Yeah just blame everything on radiation, idiot.
It's gotta be China.
I've seen the rabbits with no ears or stunted ears. Nothing to do with radiation.
You [the person who uploaded it]'re spreading the malicious rumor.
You [the person who uploaded it] are crazy. You should go see the psychiatrist quick.
Interestingly, many comments from people who take the video seriously and discuss the implications of radiation exposure (both internal and external) are flagged as "spam".