Thank you everyone for your responses. Like many things in life, it is good to know I am not alone. :-)
Just like it is an adjustment to send her off to school everyday, this new need to have time alone is something to get used to. When she was smaller she would never want to leave my side, so it is very noticable to me this new desire for independence and the change towards wanting her own space by herself.
There are two kids in the daycare that are only 5 months younger than her, but often the interests and maturity levels between my daughter and the others is way off. Sometimes they play really well and other times she wants nothing to do with them.
So I will just leave it be and remind myself of the fact that she is maturing and asserting her independence. My little girl is growing up!