Len aka Redial
I have had Basenjis since 1973, and done the apprenticeships of handling, showing, stewarding, and since 1990 judging hounds. I have four at home, one of each colour, and two boys and two girls. I am no longer breeding, but I have learnt a lot from my Bs.
As for flying, long distance, don't worry, I have flown my dogs to USA, Western Australia, and they have been in the special part of the aircraft hold that is airconditioned. I use shredded newspaper as lining for the crate, as they will burn everything for quarantine. They will perhaps piddle so make the newspaper big enough to absorb the piddle. For water, add some ice cubes made with Gatorade, or similar, for the trip. Make sure they empty before the journey, and, as soon as you can, give them a chance to potty on arrival. A kong or something similar, might give her a snack on the way, but do not feed her before the travel, save that for when she arrives. Do not feed her at one of the stops, as they often bolt when the airline staff feel it necessary to feed her.
Relax and enjoy the ride, and she will enjoy the reunion with you when she arrives at the destination.
As mentioned, in Australia no pets in the airport lounges, terminals, or aircraft. They have to fly in a special part of cargo, which is airconditioned. I have flown dogs all over the country, and international. Try and get direct flights, or the minimum of flights. The less stops the better.
I use frozen cubes with some electro lite with water, for their hydration - but not too much because of spillage. I had a dog fly from Sydney to Honolulu and was he glad to get out and have a piddle, (I did walk him heaps before the flight, and he did empty before the flight). Newspaper, for spills and something to cuddle into - don't use their blankets, as they will be destroyed by quarantine. It is okay to travel in cargo, but think of their comfort on arrival as well.
From far away, I can recommend CarolAnn near Columbus, OH, who might have or know someone who can satisfy your requirements. She has a rigorous qualification list for you to achieve, but expect it from any dedicated breeder. Good luck in your quest, and a long life for your new dog.
Sally is on the track, if you read the replies carefully you will find something that appears to have snuck in, but no where does it say to keep the dog outside, in the UK or most of the planet. You need to spend time with the Bs and see if you have affects on them as well as them on you. People including breeders, are protective of the breed, because rehousing a basenji is not always fun, because you do not know how they were treated, and it can take some months to get them relaxed again. That is why we are protective. Whatever you do, make sure you are liked by them, and you do not get affected by their traits. Good luck.
I agree with @tanza, there should never be any forced exercise until the bones 'set'. like a human baby until their skull sets, or a race horse are not allowed to race until they are two, so as to allow the bones to set. If they collapse because of their own induced tiredness, then that is okay, but never push them until they are well over 12 months, at least. You are doing right.