Carriers that are allowed in the Cabin are called "sherpa bags". Puppies are pretty easy to fly with in the cabin (must stay in the bad and on the floor under your feet). You would want to try and get the breeder to start getting the pup used to the Sherpa before you go to pick them up…. and you would want to make sure they are "really" tired before you leave for the airport...
For an adult dog, some applies, train them to the sherpa, just like you would a crate. Make sure they are "really" tired... I have flown puppies in Sherpa bags without problems....
Now they say that in a Sherpa they still need to be able to stand up and turn around .... and some airlines will check... some will not... and especially if you Basenji is really used to the Sherpa... most will not notice the size of the Basenji (at least not till you have to take them out for the "xray" and carry them through the check points..
I know someone that took their bitch to the airport in a Sherpa and she was very comfortable in the bag... the airline however didn't think the bag was big enough and made her put her in as baggage....