There is no scientific evidence that air travel is harmful to you or your baby. The changes in air pressure and humidity routinely encountered while flying do not increase the risk of obstetric complications, such as premature labour. Similarly, the radiation dose which women receive while flying is negligible and does not cause harm. Seat belts can be safely worn while flying: indeed, they are a requirement. Simply tighten the belt below your pregnant abdomen, at the top of your thighs.
Nobody can predict the future and even the lowest-risk pregnancy carries a small risk of unexpected complications.
The precise documentation required to allow air travel during pregnancy varies from airline to airline. It is always advisable to check with the individual airline ahead of travel, to avoid difficulties on the day.