We might be in similar situations. I caught the part of she is in daycare as is our dd 2 3/4 (probably about a month younger than yours). Ours is in a play based preschool, has been since she was 3 months old because both parents work way too much.
We are not pushy parents as we do not have time to be, definitely not towards academics. We definitely are a little pushy towards physical play to wear her out for bed. Despite not pushing academics our daughter has math abilities that I find amazing, and she can read a little too (I don't think 1st grade level, but a little). Her verbal language skills seem like a 5-7 year old. Her situational awareness, I think, rivals many adults.
I have the same questions. It is an unnerving situation. Our question is more leaning towards what is our daughter going to do when the academics start, and how to provide her with explanations on why other kids are not like her. She already knows exactly how to fit in at daycare, and act exactly like all of the other kids. That makes me happy and scared.
I do not want to force my dd to grow up fast, but it seems in many ways to be happening whether I would like it or not. I have found some useful advice on specific issues from this forum concerning specific things that are happening now. I have also read forums from parents of older kids, to get a sneak peek on what the future might be like. I do make sure that I spend more time with my daughter than on this forum, of course. John Lennon said "Life is what happens to you while you're busy making other plans."