Is this normal ??

I have a 2 month old daughter who is very active. She is always moving her legs and arms . She also coos , babbles, and squeels . She hs now started to "talk " to her toys and people when spoken to ,and smiles when you play with her . I am being told my family and friends that this isnt normal for her age. That she should be just lying around . My mom says she is like a 4 - 6 month old and is very advanced. Somedays I have trouble keeping up with my daughters need to be stimulated ,and run out of ideas. I play with her all the time ,and have always talked to her since she was born and while I was pregnant . Could this be the reason for her advancement ?? I was also a week late with her ,and my mom says maybe this is reasoning but I think has nothing to do with it LOL Thanks for help or ideas