I am still a New Egg, my small flock is just over 1 year old now. But one of my BO's had an injury like yours when she was 5-6 months old. I really freaked out about it and did a lot of net research. Their beaks have keratin coverings over the beak bones - like our fingernails, and grow out like our nails. If the crack goes only into this layer, then it is like splitting your nail, and it will grow out and resolve. But it the fracture goes into the underlying bone, then it will not. My chickens's crack was almost up almost to her nasal openings , so I was really worried. But she did not seem to be in pain, ate and acted normally. She continued to peck at objects and wipe her beak on firm objects as all seem to do routinely. I watched her daily, and once I saw that the break was moving distally, I was so relieved. It took a while to see it resolve, but after it did, her beak was normal. Don't know how fast their beaks grow, but human nails grow only about 1 mm monthly.
Watch your chicken's behavior, if it pecks food, drinks normally, and grooms the beak, then just watch her. But if she is not eating, pecking, then get expert advice.
Hope this helps.