How long until the pigeons go away?

Despite my best efforts to shoo them away whenever I heard them on my balcony, a pigeon has managed to lay an egg in one of my garden pots (the only one that doesnt have a plant in it, thankfully). It's sitting there now. Hopefully it can deal with the stress of me watering my plants from time to time. It seemed cruel to get rid of the egg, so I'm just going to let the dirty rat bird have it's progeny. How long will it take for the egg to hatch, and how much longer after that for the baby to grow up and go away?