I've started all my bunnies on veggies early on, Maddie about 3 months, maybe younger, and Pebble and Ebony always had them since they nibbled at Berri's (their mama). The domestic rabbit is the seem species at the wild European rabbit, which we have here, and they are eatinggreen plantsfrom babies.
All of my rabbits are perfectly healthy and I have never had even a hint ofa GI issue with any of them.

My rabbits all enjoy their veggies very much, and are all gobbled up before they even look at their pellets.
Some people like to wait until six months though, and think that's the best thing to do, I don't agree though. But you have to keep in mind that some rabbits will have more sensitive stomachs than others, so be careful.
You must start off with little bits, parsley is good, and introduce them gradually. Carrots are a treat, and must be fed like that. My girls get some carrot a few days a week, and they love it.