FMLA Question

I am eligible for up to 12 weeks unpaid leave through my work once I have my baby. I am applying for short term disability as well. When my doctor filled out my short term disability paperwork, he wrote that I will need 6-8 weeks recovery. I understand that means I may only get Short Term Disability for those 6-8 weeks, but am I still entitled to take off the full 12 weeks under FMLA?