I've been flying back and forth from the US to Europe with my various large dogs for many years, and hence have many things to say:
** In order to bring your dog to the EU (incl. Belgium) your dog must now undergo a fairly complex set of steps. Plan ahead, and consult this document (which must be brought with you, along with several vet documents):
* you must have a microchip placed under your dog's skin.
* either the microchip must be EU standard OR you must bring/rent your own microchip scanner (I found it easier to simply have a second, EU, chip inserted).
* you need a set of vaccinations for your dog far enough in advance that:
* the vaccination sheet can be sent to the USDA for a stamp (!). I had a courier do this, and that worked fine.
** United Airline's policy is to only allow one dog in the hold, and so it is wise to insist that the dog be listed in your record, and to check regularly that the dog is still in your record, so that they don't book another dog. Call the day before you leave to remind them.
**UA will also not take your pet on board if the temperature is above or under a certain level UNLESS you have a note from your vet saying that your pet can stand this variation. I have a husky mix and so I got such a note so that we could fly in winter!
** On day of travel make sure to not feed or water your dog for 5 hours before the flight.
** I'm against tranqs for the dog - it makes it harder for them to resist shocks in the plane. However, if you have a very very nervous dog, ask you vet for something that will make the dog relaxed but not asleep.
**I'm for putting a blanket (preferably smelling like you) on the floor of the crate. Do NOT put in water, as it will spill. However, do tape a small bag of food to the side of the crate, in case the flight is delayed somewhere. I also tape a large note in the languages of the country of origin and country of destination giving the dog's name, the flight numbers the dog SHOULD be on, and any care details. Then I exhort the airport staff to love her as I do -- remember there are pet lovers among airport employees, and they can be your friends.
** When you arrive at the airport, your dog and the crate will be weighed and then checked in. If you ask nicely, they will then allow you to take your dog for one last walk before being crated. This is worth it!
** When you get in the plane, ask the pilot to check that the dog has been boarded. This serves two purposes - they make sure the dog is on board, and they make sure that the cargo hold compartment is correctly heated, pressurized and ventilated for animals.
** In general, EU countries are far more tolerant of dogs in the city than Americans are. This also means that airport staff in European airports tend to be wonderful with pets -- allowing you to visit the pet during layovers, etc.
Hope this is helpful!