My husband is an only child and he too preferred adult company when he was a kid and still does to this day. His best friend is almost 20 years older than my husband.
My step sister was 12 years older then I am and when she lived at home, I hung out with her friends most of the time, also my neighborhood didn't have any kids my age to play with either. So I was most accustomed to being around older kids too. My best friend to this day is 11 years older then I am.
It seems in my experience that kids are more comfortable with the age group they are around the most. Try getting her out more, bringing her to small controlled groups of kids her own age. Join a MOPS group or something and find other moms with kids her age and invite them over for a play date, start out small and gradually work up to larger groups of kids her age. Try to avoid older more rambunctious kids at first. Join MeetUp.com and find some parent groups and attend play dates. Let them know you are trying to socialize your daughter. My meetup groups have always been very supportive, even my business networking groups have been there for me when I need some parenting advice. If you have a couple of friends with kids her age, ask them to babysit her while you go shopping or go home and watch a mommy movie, she'll play with other kids without you around, builds her confidence. I had to do that with my oldest when she was an only child. It was nice for me too. Maybe you could invite some of her classmates over for a play date, one at a time. I wouldn't go as far as to say you should be concerned or worried about her preference to older people. It's just what she is used too. I hope this helps.