GBS+ and freaking out a little

Co
When I had my first child, my son, 3 and a half years ago, my labor only lasted 5 hours. He had a bowel movement before he was born and we believe it was because he was 4 days past his due date. He weighed 8.9 and was out in 2 pushes. 
Now I'm 37 weeks pregnant with my daughter and she's expected to be considerably smaller than him. I've also always heard of labor with #2 going much faster. I found out today I'm GBS+ and I'm worried that I won't have time to get to the hospital for antibiotics. We joke about her being born in the car but now that I know I need to be at the hospital I'm getting more worried. What are the odds that my dr would induce me? (if she's not here by 39 weeks)