Putting A One Year Old up for Adoption

Is it possible to put a one year old up for adoption? how do you go about it and what are the steps. I had my son at 18 y.o got pregnant with him at 17 in my first year of college. I initially wanted to do adoption but his father was against it said he wanted to keep his son. A year later his father does nothing and helps with nothing for his son. I have a great support system but still I am depressed a year later and I regret ever having him. I would never do anything to hurt my son but I do feel I am not ready and I'm just doing this because I have to. Not because I want too.