Thank you for sending the additional pictures!
The only part I see that really says, "Basenji" to me, is her toes. The way she's standing on her feet. But, dang... I'm having a really hard time deciding what I do see in her. Basenji's form a square-ish appearance with the length of their legs matching the length of their back. Your girls back is either too long for her legs, or her legs are too short for her back. The dimension just isn't right.
Maybe (only maybe) a mix of Rat Terrier and Blue Healer?
If you choose to do the DNA test, please let us all know the results. It makes our guesses all the more fun! And no matter what you find out, enjoy this little blessing!