Is is possible my child could be different?

I have a 3 month old daughter, who since birth has been "different". She has always been significantly advanced, has hit every milestone early so far, and show signs of possibly having high cognitive function. From birth, she has always been extremely alert and aware. The nurses at the hospital were surprised how she made eye contact and could track moving objects, like she would watch someone walk across the room. She has had a social smile since 2 weeks old, she smiled back at anyone who smiled at her. She copied facial expressions since 2-3 weeks as well. She hated sleeping, she would always babble and make noises non stop at bed time and it takes her about 2 hours to fall asleep. She needs constant stimulation. She gets fussy unless she is being entertained or given a toy or learning tool to entertain herself. She has always had a very long attention span, she will sit through several books being read to her, one after another, and she loves watching preschool learning videos especially ones about numbers and words. She will attentively watch a whole 30 minute video without losing interest, and has been doing so since 8 weeks old. She remembers videos that I've already shown her, even if it was days ago. She had complete control over her hands since 6 weeks old, she found them right away and was able to look at something, reach for it, and grab it. If her binky fell out of her mouth she pick it up and put it back in. She has been holding her own bottle for entire feedings for about a month now, and she even reaches out to take it from me. She has even said "hi" back to me a few times after I kept saying hi to her. Her pediatrician is even surprised at how advanced she is. At her 2 month check-up we were told she is more advanced than some 4 month olds. I know it's too young to tell of she could be "gifted" but I was just wondering if this seems normal for a 3 month old.