Travelling by plane is safe throughout a large proportion of your pregnancy. The ideal time to fly is between 14 to 27 weeks which is also known as the second trimester. This is because in most cases, morning sickness is likely to have passed, you will find yourself much more energetic and healthy and most importantly you risk of miscarriage is low. It is however advised that you do not travel after 36 weeks in your pregnancy so if you have a holiday planned for this time you will need to re-schedule. Regardless of when in your pregnancy you wish to fly you should always talk to your doctor or midwife about your plans before hand. For special high risk cases your doctor may advise you to avoid travel throughout your pregnancy just to be safe but otherwise flying during pregnancy is perfectly fine.
Pregnancy itself is not harmful, it is a perfectly natural process but it can seem very daunting and horrific for many people especially if it is your first time.