You'll be perfectly fine if there's no complication for your pregnancy!
When I was pregnant with my first kid, my job required up to 100% traveling. So I asked my ob. to write a note to my boss that I won't be able to travel during my pregnancy. However, my ob. refused to do so and said it's ok for me to travel til 32 weeks!
I think a lot of pregnant women still takes long flight and I think it would be safest to do so during the 2nd trimester (4-6 months).
I had a friend flew from SFO to Singapore when she was pregnant. Also, once I had picked up my pregnant coworker from the airport, but she only carried her lightweight laptop and checked in everything.
我4個月由美國飞sydney.... 一齊安好。。。just relax...n go toilet frequently... drink plenty of water... best to bring an empty bottle n have the FA full it up so you can have plenty of fluid on the plane. Have fun n enjoy