I don't think the OP is on the same page. She just has a girl dog that she likes and thinks it would be neat to have some pups. She is obviously not aware of health concerns in the breed. Sorry to sound condescending, but I think the only unusual thing about this is that she has come on a forum and asked, instead of just finding some male and getting on with it…...possibly because it isn't so easy to do with Basenjis. You can't count on finding a willing dog owner in the breed to provide a stud.
I know of quite a few people with purebred pets who at some point or other get the idea they would like to have pups from them. Yeah, backyard breeder, and many say it with contempt. They don't do research, skip the important health tests, and just go ahead and breed. However, sometimes it works out well, the resulting offspring get good homes, and everyone involved is happy with the outcome. Everyone knows the other possible outcomes, with unwanted puppies or heartbroken owners who picked up a cheap pup with health issues.....