how do I file for disability/maternity

Sa
With my job I won't have disability coverage for my pregnancy. I started after I was pregnant so I can't take out the policy. I'm trying to figure out when and how to file for disability through my state NY. 
Can anyone explain the process to me. When should I file and how do I file. I'm due January 8th but you never know. I'm worried about $$ while I'm not working. I plan on a vaginal birth so I know that's 6 weeks.