Hey Loula,
as my name suggests, I work in the industry and I would go with what your docs say. Most airlines I've worked for have no issue with flying when you're pregnant. Often the rule states you can fly up to 28 weeks without doc letter, between 28 and 32 you provide a letter from doc, stating it's a single pregnancy, without complications. After 32 you can't. If your docs happy with it, don't miss out

Saying that I know one carrier in Oz that allows their cabin crew to fly themselves v. late into their pregnancy.....that's stupid as they're primary reason for being on board is safety of the passengers - and they'll be naturally thinking of themselves and their unborn if there was an emergency...but I digress!