any information you'll get on a forum is going to be anecdotal at best. Write down all the countries you're going to then locate the nearest Embassy or Consular office to you. Call them, and ask to speak with someone knowledgeable about import/export regulations ( you will be doing both, right?). Do not, I repeat DO NOT ask the person who answers the phone your question. They will be a clerk, almost always someone local, (they won't relocate secretarial staff to a foreign posting generally), and they will have no idea. They will often just give you an answer, right or wrong to avoid finding who you need to talk to.
Once you have your answer on the phone, get their address, email, and phone number, and ask them to send you written confirmation of their interpretation. Without it, you're wasting your time. If you can talk them in to sending you a written interpretation (good luck with that, BTW), take it with you.
The Phantom has been available for over a year and a half, worldwide. Almost everyone has seen them at some point...DJI did a pretty good job of pushing it on the global retail market. There are pretty good odds that someone within the Customs office you've arrived at will have an idea of what they are.
A couple of things you have to keep in mind, though; batteries and permission to film. You have limited numbers of LiPo batteries that can be shipped, it is based on weight, not numbers, and you may very well need to ship them separately as dangerous goods. Again, check with each countries' Civil Aviation authority, and ICAO regulations regarding this.
Lastly; permission. There are a number of countries around the world and several in Africa that are quite "sensitive" to foreign nationals filming in their country. It often has little or nothing to do with "national security"...there are many many Officials who supplement their income through the issuance of a variety of "permits". It's irritating, it's offensive, and it is the way it is; you don't have to like it; you just have to comply.
One last suggestion; if you're doing this for fee or expect to sell some or all of this footage...re-think your plan. That constitutes "work" and you would need a work visa to shoot. DON'T RISK IT!! Many companies have serious penalties for things like that, including denial of entry, fines, and/or imprisonment. They do not have ANY sense of humour about things like that. if you shoot, it is as a hobby, for personal use only. That's your story and STICK TO IT.
I've worked in a number of countries in Africa and the importation of any number of things is an "adventure" to say the least. I hate to say it, but coming from North America or Europe, you're viewed by many as being "rich". if you're "rich", you can afford some additional "administration" fees