D.R.
Hi, S..
Your daughter sounds perfectly normal. In fact, how wonderful that she enjoys playing independently! I taught preschool for 10 years with 4 year olds. This is the time when kids begin to play interactively, rather than the parallel play of two and three year olds. (two children side by side playing-not much interaction). She must enjoy being with you and her sister, which is great! I'll bet if she's with one or two other kids on a play date at their house with you not there, she might interact more. Or, it could be that she is a little shy, which is perfectly fine, also. She is lucky to have her little sister and you as built -in playmates.
I would observe my son and daughter when they were little and sometimes I worried that they were not as outgoing as I am (which is my issue, not theirs :-). They are now 12 and 21 and are amazing people with friends, but they also enjoy their alone time.
Enjoy this sweet time while you have them with you. Play as much as you can with them. They'll grow up so fast. When she seems ready, just have one other child over to play. I'm now a play therapist, working clinically with kids who are stressed out and sometimes overloaded with activites with other children.
Best of luck to you!
D.