Bunnies can’t puke, so this brown liquid is poop. If it doesn’t stop more or less right away, take the bunny to a vet. A healthy young bun may have sticky poop, but liquid poop is often a sign of a parasite that’s very common in rabbits (coccidia) and can cause the death of a young bun through diarrhea and dehydration. It can be cured with the proper antibiotics. Another possibility is bacterial enterits, basically an inflammation of the large intestine. That too can become fatal in a very short time.
If the liquid poop is a one-time thing and there are other, normal, round poop as well, the bunny eats and drinks and acts normal, this could have been a tummy upset caused by the carrot. carrot can be difficult to digest for some bunnies (I have one of those bunnies). Stop the carrot and encourage hay-consumption, lots of hay and water is the best things when your bun’s tum is out of order.