I have an 11 year-old relative that seems to have developed a major fixation on my new husband. Her behavior (which makes both my husband and me uncomfortable) began shortly after he and I got married. She has asked me to close my eyes so she could kiss him on the shoulder, hugged him repeatedly (at least once per hour) when not doing so for any other family members, sat in front of him cross-legged wearing only a long t-shirt and underwear (she was told to cover up by her sister), requests frequently (that I have heard) to see him (he is currently on a 9 month deployment), asked me for a picture of him, followed me around when I Skyped him so that he could say hello to family at Christmas, tried to take over the Skype conversation when I was talking to him to the point of almost climbing into my lap. She also treats her doll as though it was real. She mentioned that her doll is grouchy if it does not get at least a 3 hour nap. When I went to her grandparents' house at Christmas, she opened the door a crack and stuck the doll in the crack and did nothing else until her grandmother told her that it was cold out and to let me in. My husband has a background in psychology and social work and some of her behaviors make him very uncomfortable. She also has had a speech impediment (a lisp) since she was young. Both of us find some of her actions to be less mature than most girls her age. We wonder if this is normal or if there could be something wrong.
Behaviors that you describe are not developmentally appropriate for an 11-year-old child. Seeing her pediatrician for an initial evaluation would be a good start.
In the mean time, don't be afraid to set firm limits as a wife.