What i took from the film is that the doll wasn't alive, that it was just a conduit,it wasn't animate or anything... Why then it's there one single moment where it appears animate and alive with bloodshot eyes in the priest's car?
Probably the same reason that nothing but the doll was shown levitating in the baby's room in the other scene. The Demon, or Annabelle Higgins, whichever you prefer, was probably there making the doll do these things, but the audience couldn't see it because it would look silly or less scary to show whoever was actually controlling it.
"He came home." - Dr. Sam Loomis from the original HalloweeN
Actually in the scene where Annabelle "stands up" and levitates, into the air, the camera pans into Annabelle's face BUT you can see a faint image of the demon's face behind her! Rewatch that scene- it freaked me out. :)