I'm going to go against the grain here and say I have flights booked for week 22 and a return in week 23 of pregnancy, I am unvaccinated, and didn't even consider not flying :/
I live in Germany and for various reasons have been regularly flying to and from the UK throughout the pandemic (all completely legally while following every quarantine and testing requirement), so I guess I've been desensitised.
Plus the current policy in Germany (at least in the state where I live) is that pregnant people should not have the vaccine, so I couldn't get it even if I wanted to.
So my experience of flying during the pandemic has been very reassuring ... everyone wears masks, the cabins are deep cleaned between each flight, about 60% of the air circulation is being replenished from outside while the remaining 40% is filtered, and nowadays everyone has had recent negative tests or is fully vaccinated.
In fact there was an article in a journal from last year that claimed that the risk of contracting covid during air travel is lower than from an office building, classroom, supermarket, or commuter train.
This obviously isn't saying there's no risk, people have done and will still catch covid from air travel, but you could equally catch it on a train. So my advice would be to do what feels comfortable for you.