Can I get full custody of my son?

My sons father is not involved in his life, he might see him once a month iff that. he gave me 80 dollars the beginning of may but he doesnt usually help out he doesnt buy him diapers or anything. I lost my job and he didnt even offer to help out. My son calls another guy dad because his dad is not around, My son does this on his own I did not force him to call him dad. my son is 14 months and he is afraid of is real father he crys and he does not know him. I try to get him to be involved but hes always to busy. His own mother said I should take him for child support. Could I get full custody. If something happens to me his father is not stable enough to take care of him what do you think?