California unemployment law is quite strict, as it is in most other states.  This is to prevent unemployment insurance fraud and eliminate individuals from collecting unemployment and working.  In California, you are required to file on a continuous basis proof that you have attempted to seek employment and file an affidavit to that effect.  You may still be able to collect while partially employed but once you quit (prior to the three month contract end date), you will undoubtedly be scheduled for a telephone interview to determine if you are eligible to obtain unemployment.  Further, if you obtained this contract as an independent contractor, you need to find out whether this breaks any claim you originally had when you were collecting unemployment and if now you don't qualify because you are no longer an employee.  You might qualify for short term disability due to your pregnancy and giving birth, but check with California's Employment Development Department for both unemployment and disability insurance.