To get induced?

Today is my due date (9/11). My dr wants to schedule me for induction this Sunday night, 9/17 because the practice I go to has concerns of low functioning placentas after 41 weeks. I asked if we can give him a little longer to try and come on his own and she said we could strip my membranes on Monday the 18th but then she'd want to only give me until Tuesday night 9/19 and then be induced. Any thoughts? I wanted to try and give him more time to have him naturally but I also don't want to risk the placenta crapping out on the baby! This is my first pregnancy and has been healthy so far.