Short Term Disability?

So I plan to take short term disability while I take my maternity leave from work. I’m hoping to be able to do the full 12 weeks covered by FMLA. Is short term disability something I can get squared away before I give birth? Or is it something I can’t claim until baby gets here? And I’m not talking about getting paid right away, just getting things in line so when baby does get here I’m not juggling a newborn and trying to get that settled. Any advice?