To answer the original question, NO. the average two year old does not follow directions so well, carry on conversations and respond to a doctor's office visit that way.
As for the question of preschool, I would suggest going to see two or three different places. Ask to observe for about an hour. Don't take your daughter. Watch the other kids and see if there are any you feel are acting and talking like she does. Get a feel for whether your daughter would be happy with the activities they do there, the schedule they follow, etc. Don't worry about whether they teach gifted kids there. She's young. She's got lots of time and lots to learn. She'll absorb and learn from her environment whether it is formally taught or not. The important thing at this age, IMHO, is that the kid is happy because she fits in and the adults understand and like her.
Good luck in your search as well as coping with the GT denial!
