S.B.
Dear Y.,
Typically, state disability covers approximately the 6 weeks following a birth, but can be longer if it's found to be medically necessary due to complications mom experienced. The rate of pay is based on your income during your "eligibility" period, as another mom suggested. You can get more information about that at the www.edd.ca.gov website.
You may qualify for more time off under the Family Medical Leave Act since you need time to care for your premie baby. The downside is, not all employers have to grant it if there are less than x amount of employees and you don't receive pay during that time. The upside is that you get the time you need and you can still remain employed. Things may have changed, but that's the way it was when I looked into it. Information regarding the FMLA should be on the EDD site as well.
Hopefully, your employer will be understanding and work with you to give you the time you need.
Take care of yourself and your precious baby.
Best of luck to you!