Ideally, a calf should be dehorned shortly after birth. Back when I raised calves, we used dehorning paste for the job: You shave the area around the horn (where it would be when it starts growing, because baby calves don't have horns yet) and apply the paste. We just didn't get around to doing that with Jody. So she will have a headache for a few hours.
If you wonder why I wanted her dehorned, for one thing it makes her worth more if I sell her. Also, a cow can hurt you with her horns, not meaning to do so: Old Suzy, my first milk cow, once swung her head at flies while I was petting her and gave me a black eye.
Besides, they're prettier without horns.