When do doctors begin measuring fundal height? is it reliable before 20 weeks?

About 12 weeks: It begins to peek out from under the bones in your abdomen and it's height can be followed.

20 weeks gestation: In clinical practice, recording the actual fundal height measurement from the palpable top of the uterus to the superior edge of the pubic symphysis is standard practice beginning around 20 weeks gestation. Most caregivers will record their patient's fundal height on every prenatal visit. Measuring the fundal height can be an indicator of proper fetal growth and amniotic fluid development.