If you think that Medjai is an exemplary example of the breed, then the next step is to try out some venues so that you get to involved in the basenji community and get to see other basenjis and their owners and breeders and your basenji is seen by other basenji owners and breeders. This will give you a chance to research what qualities will be a good match for Medjai and what he has to offer the breed. Start with a fun match if you can find one or perhaps there is someone on this forum in your area that can suggest a show that they will be attending where they can help you out. Or attend a lure trial and give Medjai a chance to practice.
Medjai will need to be at least 2 years old before you can get the health testing that the Basenji Club of America considers to be the minimum recommended health testing: Hips, Eyes, CERF, and Fanconi. So while he is growing up this is a good time to get out there and get to know your local basenji community.
It is important for breeders to be active in the basenji community and see the other basenjis that are out there. It is very easy to become kennel blind, where you see all the great qualities in your own dogs but overlook their faults. Participating in events like coursing, conformation, agility, etc helps to keep us more grounded and see structure in action which is important in evaluating a dog.
Once you have done all of this you can start to think of breeding. Even then you will need to be prepared for the expense and responsibility of breeding a litter. I was told when I first got involved in this breed that anyone who ever considers breeding a litter should first put in time as a rescue volunteer. Once you have helped to place homeless basenjis and see why basenjis end up in need of rescue, and how many need homes, if you still feel there is a compelling reason for you to breed then you might be ready to breed a litter. Having been a rescue volunteer and now as a shelter volunteer, I wholeheartedly agree that anyone who plans to breed a litter should have to do this. Pet overpopulation is a serious problem in this country and will only get better with both owners and breeders taking responsibility for their animals.