For one thing, YEARS ago I actually tried this with a bunny of the same age. It was a terrible idea, and I'm really ambarassed to even share that I did it. But, I'm sharing it as a help to other buns. The one I did this with lived several weeks and then died. These rabbits are made to & and used to living in the wild. It doesn't matter how old (or young) they are, or what you feed it. If it really is a docile as you say however, I would really worry about it, there's a very good chance it had some sort of disease. Not to be a party pooper, but I'd find a rehab ASAP or release it if there is not one nearby. Looking in the best interest of the bunny, that it the best option.
One more thing, recently I rehabbed a litter of 8 cottontails. They did GREAT. Or so I thought. As it got closer to the day I was going to let them go (4 weeks of age) they were growing, eating solids, doing WONDERFUL. Then, the morning I was going to let them go, I go to get them out of their cage, and all except 3 had died. No change in care to speak of, but they died. They had gotten to the point of being stressed in the cage and it was too much for them. Even though me caring for them was all they'd ever known, their instincts told them to be scared of me and it did them in. On the other hand, the 3 I released have thrived and I've gotten to watch them grow up in their natural environment they were designed for. For months now I've been able to see them every few days (sometimes every day) in the back yard hopping through nibbling the lawn. They won't come to me, just like any other cottontail, but they live in the area.
The bunny in the picture shown is definitly old enough to be on its own. Once they weigh 100 grams they'll be fine on their own in the wild.