I've had some classes in psychology, but I am by no means an expert, but here are my thoughts from what I remember from my classes (its been awhile).
Let me address your second question first. Your best bet for an evaluation would probably be though a psychiatrist. They are really the best when it comes to diganosis and evaluations. Make sure you get one that specializes in children and/or teens because they will have the skills needed to work with and 11-year old. A referral will be needed from a primary care physician like a family doctor or a pediatrician most of the time, most psychiatrist require this. You can often find good pscychiatrists at many children's hospitals/medicals centers if you are close to one.
Now, for your first question. Yes, an 11 year old can show signs of a personality disorder, but it can be hard to diagnose. Mainly because chiildren are deveolping and changing so much at that age. As I am sure you know, a child's brain development changes so fast. Plus, an 11 year old is entering puberty and the body's chemistry is changing as well.
Also, many signs and symptoms that a child displayw can be attributed to many different disorders that it is often difficult to figure out what the proper diagnosis is. Often, it isn't clear until the late teens or early twenties what the proper diagnosis is, This can be so frustrating for parents and caregivers.
Also, the guidelines for diagnosing many mental illnesses prevent doctors from diagnosis some illnesses until a child reaches 18. So, the 11 year old you are talking about may in fact have a personality disorder but may not officially daignosed as such until the age of 18. Until then, there may be a broader, more generic diagnosis applied, but I cannot remember what it is right now.
I don't know if any of this makes sense, but I hope it helps. Good luck.