B.M.
If you are talking about state covered disability, I don't know - I live in a state that does not offer disability.
As far as your company you will have to check with your benefits department. It varies from company to company - but MOST companies have a waiting period, although some offer disability immediately. Sometimes short term disability is paid for by the company and sometimes it is an election that you have to choose when you enroll in insurance and then you pay a monthly fee.
HOWEVER - not all disability coveres maternity. You will have to check on what your employer offers. Also, the amount that you get paid will vary - most of the time you do not get 100% of your salary AND on top of disability you have to pay your own insurance premiums.