Thanks for all of your replies! Rex just had his first vet visit (first with me at least), and he was given a clean bill of health. The vet that I saw also agrees with a lot of you that he looks like a Min Pin more than a Basenji, but he is likely still mixed with something because he's a bit too big to be a pure Min Pin.
I've looked at a few DNA Dog Breed tests online, and they seem to range in price and in quality. It seems like some of the cheaper (~$50) tests are fake, but they go all the way up to almost $250 for the higher quality ones. Do any of you have experience with these DNA tests / have a brand you found reputable? I'll be sure to post the results of any of the tests with this forum!
Thanks again, and Rex is doing really great in his new home!!