i recommend you look over some diet info. there are many veggies that bunnies can safely eat. there’s great info on the BB diet page: https://www.binkybunny.com/BUNNYINFO/Diet/tabid/60/Default.aspx
also a very comprehensive list of good and bad veggies. i have a copy printed out that i keep in my purse for when i go shopping: binkybunny.com/Default.aspx
like BunnyLiz and nikiway said, carrots are okay to feed, but only in strict moderation and as an occasioanl treat. treats should not be fed more than 3x per week. there is a picture on the BB diet page that demonstrates what a proper bunny treat would consist of:

the most important part of the diet is hay, followed by greens. it’s recommended that bunnies get betw/ 2 and 4 cups of veggies per day, so it makes up a major portion of their diet. it’s most like what they eat in the wild, and it helps to hydrate their systems. limited pellets help to fill in the nutritional gaps, and are fed in very tiny amounts. another diet article i like: http://www.bio.miami.edu/hare/diet.html
i do hope this helps. personally, my bunnies love red and green leaf lettuce, endive, escarole, romaine, dandelion and collard greens, parsley (both kinds) and cilantro, watercress, carrot tops, and the list goes on. they get 4-5 different types each day, the same ones for about 4-5 days, and then i go to the store again and we get something else. they enjoy the variety, and i get such a kick out of watching them dig into a huge pile of greens.
you will need to introduce new veggies slowly, one at a time over the course of a few days or a week, but once they are used to the veggie, it can be rotated in and out, usually without an issue.