First, just be aware that because your basenji got along with another dog doesn't mean she'll accept a new companion, much less a female. That said, I understand the sentiment.
Have you checked with BRAT (Basenji Rescue & Transportation) or even Florida's rescue, CampBasenji?
http://www.campbasenji.org/
They only list 2... however she has several more that will be ready soon. Pam let's no dog go until she has had them for a while in foster, has a very good idea about any behavior issues and works on them, and their health needs addressed: http://www.campbasenji.org/available-for-adoption/
Brat also only has 2 listed, but I am sure there are more:
https://www.basenjirescue.org/dogs/default.asp
https://basenjirescue.org/dogs-mixes/default.asp
While it makes finding a rescue harder, I am glad we are not as overflowing with byb/puppymill breeders like before. But there are rescues out there. Good luck