First off, don't worry about the plane trip being dangerous to you or the baby. As long as you are in good health, and the pregnancy is progressing normally, you are safe to fly up until the end of your third trimester (usually 36 weeks - 9 months). Air travel does not increase the risk of miscarriage or pre-term labor, and poses no other risks to mother or child.
It is the last four weeks (once you reach the 9th month - 36 weeks) that women are usually prohibited from flying. This is because after 36 weeks, a women can go into labor at any time, and the airplane is not made to handle such situations. For one, there is no guarantee that a doctor will be on board a plane, plus, should any complications arise during the labor and delivery, the plane does not have the medical equipment to handle such situations and it could put the health of the mother and child in danger.
Before you travel, you will need to get a check-up from you doctor. You will need to tell them that you plan on traveling so that they can properly asses your condition. If you are past 27/28 weeks (7 months) they might also have to write out a medical certificate for you stating that you are healthy, the pregnancy is healthy, and that they do not anticipate any problems with you being able to fly (depending on the regulation of the airline you plan to fly with).
The FAA has set up the guidelines for pregnant women and air travel. FAA Airline regulations state:
Obstetrical patients are free to fly, but pose a significant risk in later stages of precipitating delivery during flight. Pregnancy past 32 weeks should be carefully considered for restriction from flight and must be accompanied with an authorization note from a doctor. Those past 36 weeks should be prohibited from flying unless personally accompanied by their doctor. http://www.faa.gov/other_visit/aviation_industry/designees_delegations/designee_types/ame/media/Section%20II.7.1%20Transportation%20of%20Patients%20by%20Airline.doc
I looked for the official rulings of the CAA and EU, but they leave that ruling up to the individual airlines. Here is a good site that will let you look up any airline (and/or airport): http://www.airlineandairportlinks.com/lines_by_name.html
Like I said earlier, the FAA has set up guidelines about pregnant women and air travel, but all airlines make up their own rules and regulations regarding pregnant women. Some do not restrict travel at all, no matter what stage of pregnancy a women is in, and others start to restrict at 7 months (27 weeks), although the majority restrict around 36 weeks (9 months). You will need to check with the specific airline you want to fly with to verify their stance on flying while pregnant.
Please keep in mind that if you are flying pregnant, especially in later pregnancy, you are not guaranteed passage even if you bring a medical certificate from the doctor. The final decision to let you board will be left up to the captain who will be informed by the gate crew of your status. If for some reason you are denied boarding, please do not feel that it is a reflection on you or that the airline is bad. They are only trying to do what is best and protect you from any dangers (such as pre-term labor) that may arise during the flight. Remember, a plane is not designed to handle medical emergencies and they have a limited amount of medical supplies on board. It is very dangerous for a baby to be born in-flight because planes are not equipped to handle that type of situation. Flight crews have minimal medical training at best, and there is not always a doctor on every flight. Should there be any type of complication, planes just do not have the capacity to deal with it. That is why there are restrictions for pregnant women when flying.
While traveling, I advise that you keep you medical records (for this pregnancy) with you at all times. You should also get the name and number of a doctor where you will be visiting/staying in case any type of emergency should come up.
I suggest bringing your own snacks from home. They will be healthier and you'll be used to them. New regulations allow you to take beverages (including water) from home as long as they are less than 3oz (100ml), -OR- beverages (including water) of any size that you have purchased from inside the security area onto planes. You are also allowed to bring a limited amount of yogurts, cheeses, puddings, etc from home as long as they too are in containers of 3oz (100ml) or less.
Some healthy snacks to bring include raisins, granola bars, yogurts, cheeses, dried fruit, etc. I also highly suggest bringing along a packet of TUMS to help with any heartburn or indigestion you may have.
Another thing that gets asked a lot when talking about traveling while pregnant is what does happens if the baby is born in-flight?
Citizenship is membership in a political community and carries with it rights to political participation; a person having such membership is a citizen. It is largely coterminous with nationality. Citizenship is the political rights of an individual within a society. Citizenship status often implies some responsibilities and duties under social contract theory. Citizenship derives from a legal relationship with a state. Citizenship can be lost, as in denaturalization, and gained, as in naturalization, or by marriage. http://en.wikipedia.org/wiki/Citizenship
Most countries have rules set up so that the child will only acquire the nationality of the parents, such as the rules of many European and African countries. That means that just because a baby is born on a Belgium plane (for example), the baby would not receive Belgium citizenship unless at least one of the parents was Belgium, or the family had been living in Belgium for a period of some years. The baby would only acquire the nationality of the parents. Since the article says the mother is Congolese, the baby would also be Congolese. This is known as Jus Sanguinis. http://en.wikipedia.org/wiki/Jus_sanguinis
The US (along with a few other countries) has laws set up so that a child born on a plane inside the US, or flying over it's territories would acquire US citizenship. In cases where the baby is born over US territories (and the parents are not US citizens), the baby would be born with dual citizenship - the nationality of the parents, and American citizenship. This is known as Jus Soli. http://en.wikipedia.org/wiki/Jus_soli
http://foia.state.gov/masterdocs/07fam/07m1110.pdf Section 7FAM1116.1-3 AIRSPACE paragraph a
In the case of Belgium citizenship, citizenship is actually based on a mixture the principles of Jus Sanguinis and Jus Soli. In other words both place of birth and Belgian parentage are relevant for determining whether a person is a Belgian citizen. It is regulated by the Code of Belgian Nationality. In some circumstances citizenship is granted to children born in Belgium to non-Belgian parents. This is not the case where parents are temporary or short term visitors. http://en.wikipedia.org/wiki/Belgian_nationality_law
Even if a baby is born in a plane, there have only been two recorded incidents where the baby was allowed free passage for life. This is a rarity, and NOT the norm.