CA Unemployment/Disability Insurance

I work in the Television industry. The show I work on went on hiatus for the summer (as most do) so I've been out of work and on unemployment since mid May. I'm due in early September. 
   Has anyone had experience w/ switching from unemployment to the disability insurance before giving birth? If I'm not mistaken, aren't you supposed to file your claim like 7 weeks before you're due? 
    Any info would be helpful! Thanks!