I have done some research and know that you can breed pigs with carrots. How do you get carrot seeds to plant carrots?
You need to keep on killing zombies, until you get one from them. Then, plant the carrot in hoed/tiled ground (grass) and wait until it shows orange at the bottom. Finally, harvest it and it should drop 1-3 carrots. Once finished, just repeat steps 2-3 for more carrots
The carrots themselves are the seeds. You can just plant the carrots you have, then they will grow and "duplicate".
Unlike Wheat, planting carrots requires that you have carrots already, which is kind of a catch-22 if you have none to start with.
Carrots were added to PE in 0.8. (December 2013) as a rare drop from Zombies.
Once you have a single carrot, planting it and then harvesting it when fully grown will drop 1-4 carrots, so from that point onward you're likely to get them faster from farming.
In order to get carrots, you must kill a zombie. After you have killed the zombie, you simply till the ground and plant the carrot in the tilled ground.