flexible due date?

So when we found out I was pregnant, we had been trying to a long time, I had everything marked on a calander so my original due date was April 20 by last cycle. First sono showed due date was the 18th, then at 28 weeks for anatomy scan she was almost 4 lbs and showed a new due date of April 7! Doctor keeps telling me she is a large baby and that by April 13th he will induce me which would put me at 39 weeks according to original due date 4.20.