How accurate are the doctors when they tell you a due date judging by the fundal height?

You are not given a due date judging by the fundal height.

A comparison of your size with length of pregnancy may be made by measuring the fundal height with a tape measure. After 20 weeks the length of pregnancy corresponds with the measured fundal height in centimetres. This is fairly accurate if done by the same person each time. More importantly it shows if your baby is maintaining its growth. For example if you measure 20cm at 20 weeks, and then at 30 weeks you only measure 27cm your baby is not growing at the normal rate. It can also show if your baby is larger than average.

Both small and large babies may have trouble at birth.