Airlines are cracking down on "service" animals. Because of the vast abuses by many, don't count on being able to say a service animal on more and more airlines without a boatload of documentation. I think eventually they will restrict to certified trained dogs only and exclude emotional support animals to incredible rigid qualifications. I doubt puppies will be allowed.
However, for your question, every dog is different. I would imagine doing it so often with lots of socialization, most stable dogs will be fine. A basenji from a responsible breeder is critical for health and temperament. Be aware the adult size of a basenji may already limit airlines you can use.
https://www.washingtonpost.com/news/tripping/wp/2018/01/22/delta-is-tightening-restrictions-on-service-animals-its-about-time/
http://traveltips.usatoday.com/airline-restrictions-pet-travel-15638.html