K.P.
I believe that you can only collect unemployment if your former employer "paid into" the system on your behalf. Most employers do not provide such benefits (think of it like health insurance) to part-time employees.
Each state is different, though. My husband resigned his position in NY to move to FL with me and the children. We assumed that he would not be eligible for unemployment because he voluntarily resigned... wrong! Because my new job was an "unreasonable distance" from his position, they allowed him to file.
Go online and fill out the application. The worst thing they will say is "no".