They can be very wrong at this point about weight of baby so don't worry about that. Really once you hit 36 weeks you could go at any time so of course as always throughout pregnancy watch for signs of labor just because it's early doesn't mean you can't go at any point. Good luck!!
Ive been measuring a week ahead the whole time ive been pregnant. Unfortunately at this stage in pregnancy, the measurements are not always accurate. With my first son the dr. was convinced he was going to be 9lbs or more, wrong, he was 7lbs11oz. I wouldnt worry too much. I am due feb 24th. As far as labor signs, regular contractions that dont go away with hydration or rest, pelvic pressure, spotting or blood tinged mucus, are a few. Good luck.