This is an observation rather than a criticism: the woman playing young Carrie appears to be channeling the Sarah Jessica Parker interpretation of the character.
Ummm... Why wouldn't she? Isn't SJP the character she's playing?!
No, she's playing the character of Carrie Bradshaw... the actor on Sex and the City
was Sarah Jessica Parker. Her inflection, delivery and general presence was an excellent impression of Parker's Bradshaw. And maybe that's what the producers wanted.
It's kind of like Karl Urban in Trek 2009. He was great, but I felt more as though he was doing an impression of DeForest Kelly's version of Bones than bothering to come up with his own interpretation of the character. Which is fine... again, not a criticism, just an observation.