Hi there,
The usual procedure is to phone the caa, who will temporarily suspend your girlfriends medical. Nowadays under JAR rules you can fly up to 26 weeks of pregnancy as long as you are considered fit to fly. You are sent a letter by the caa outlining the procedures you must follow. You must be free from a variety of symptoms i.e morning sickness, episodes of bleeding etc.
Then in conjunction with your ame and midwife you must provide a report ( i think it is monthly) indicating your fitness to fly. At any time if your midwife, ame, the caa or you yourself consider yourself no longer fit to fly your medical will be suspended and you cannot get it back for the remainder of your pregnancy.
You will normally get your medical back after a successful 6 week check up following your pregnancy. This length of time may be extended following a ceasarian for example.
You may need to think of alot of different things when you're pregnant that might be affected by flying i.e the health of your baby. I was advised against flying by my doctor for reasons of additional radiation, the fact that your body is effectively sitting at 8000 feet or so for hours a day and the subsequent physiological effects. Also you are more prone to dvt when you are pregnant, and as its not unusual to do an 11.5 hr shift in my company thats a fair bit of sitting down.
You may have to consider the hopefully unlikely event of something going wrong on a flight ie decompression, fumes in cockpit, and actually having to get out of the aircraft via the window when you are much bigger than usual!
One final thing, some airlines won't allow you to fly at all when you are pregnant so the element of choice may be removed altogether. Its very much an individual thing whether you decide to carry on flying, but as you have only just found out about the pregnancy its worth speaking to someone in the know ie. doctor or midwife as they may have valid concerns you may need to consider. Above all else Good luck to both of you!
ps getting away with no morning sickness is dead jammy!