There is no legal or even internal policy restrictions for pregnant women. That is a judgement call determined by the expectant mother whether she will risk being so close to her due date. If she expects to go into labour at anytime within those few hours of the flight, she 'should' not fly.
There are no health risks involved unless she suffers from high or low blood pressure. Pressure and Oxygen levels in an enclosed airplane are monitored and regulated throughout the flight.
As an airline pilot I find these answers a bit, wrong. Pregnant women fly all the time, usually it's not advised during the last few weeks do to the lack of professional medical folks. The airlines don't like the thought of having to divert a flight, nor the entertainment for the pax. & the mess left behind. In 20+ years I've encountered a birth once. The female was Mexican & spoke very little English, we found later that she'd been asked how far along she was, she wasn't sure or misunderstood the ?. The FA called me back, she & a few pax. moved to the rear & held up blankets to shield the view, we landed asap, & boy did I feel sorry for the clean up crew