Just so we're all clear, when you say you know how to raise pigeons, but you only have one?
Pigeons are altricial, not precocious. They more resemble a finch, sparrow, or robin when hatched, and will need to be fed with a crop milk substitute every hour during three daylight hours for at least the first 5 days.
Paradise Aviary on YouTube has an excellent description of how to do this for finches and parrots. The formula for parrots is likely good enough for pigeons, but maybe read up before you take my advice.
Baby pigeons won't self feed for at least the first 18 days, possibly closer to 25 to 30 days.
The single pigeon you have is unlikely to go broody just by itself. Typically they raise two eggs at a time, with pair parenting. The mother does most of the brooding with the father taking a turn for a couple hours a day, tipsy around midday. After around 15 to 18 days the father takes over most of the feeding and caring as the mother gets ready for the next pair of eggs.
You mention that there are others in your area with pigeons. Typically young pigeons are available from around mid April until late fall or mid winter, depending on when the owners stop letting them breed.
The usual way to acquire pigeons is via young, recently weaned birds rather than as peeps or eggs.
My apologies if you're already aware of this. It just sounded like perhaps the reality of the care level required in the first several weeks maybe wasn't obvious.
