I was pregnant with twins and one of them was breech up until labor. I was having labor contractions and went to the doctors and they said I had to get a c section. I told them to wait. And what do you know by the time it was time to push both had heads down. Pushed them out naturally with no meds. Beautiful.
It is common for babies to be breech- some turn right at the 'last moment'. It really depends on your doctor, how long they will let you go for- some will let you go longer. Also, there are many resources out there to try to help turn the baby. Some doctors will go for this and other's won't- I'd recommend looking up some resources on that and having a conversation with your doctor to see where their expectations lie on this. Good luck!