My 5 month old bunny enjoys romaine lettuce, leaf lettuce, parsley, cilantro, and dandelion leaves as veggies. As fruit treats she loves apple, banana, carrot (fed infrequently like a fruit).
I've been giving her veggies since about 4 months old and she has tolerated them well. She has a lot of calcium in her urine, so the vet recommended more veggies/less pellets.
I give her lots of Timothy Hay and have been mixing other hays like have been mentioned above. She has Timothy pellets, however I do not limit them---if it's a baby, they should have unlimited pellets. But, my rabbit prefers to eat the veggies and hay, and then the pellets. She seems to know what to eat to balance out her diet.
Babies should have alfalfa hay, (more protein and calcium for growing buns) but I started mine on Timothy earlier because of her calcium issues. However, I think the vet was not rabbit savvy and it seems young to take away the alfalfa. I have just started feeding a small amount to her a couple of times a week in addition to her other hay.
Everyone seems to have a different opinion on whether rabbits should be fed pellets. But pellets provide essential nutrients and vitamins and are good to at least have a small amount in the diet, and especially for young bunnies to have a lot.