I am hapoy to help you with your question. You say schizophrenia runs in your family ,and yes there is a genetic component to developing this disorder. However, it could be that your daughters "loner" personality is just that, an introvert and her talking to herself is not that uncommon, children do that. Depending on who the relation is that is schizophrenic that chances are higher than the general population. For example: If its a first degree relative, a parents, siblings then the risk is higher than if it's an aunt,uncle, cousin, nephew etc.
Schizophrenia can appear in childhood but it is very rare, it's not until adolescence that symptoms may appear. At 11 she is on the cusp of adolescence, but if it would ease your mind I would suggest you do some reading on schizophrenia.com. and if you still have concerns after reading that you have an evaluation done by a psychiatrist.
I hope this helps and gives you some direction.
There is so much new information regarding heredity and studies regarding this disorder. If your concerns are troubling then talk to her pediatrician and ask their advice. If she/he thinks she'd benefit from being seen by a therapist or psychiatrist then take her. If there is a history of mental illness in both families that can be explored in therapy and hopefully ease your mind. It is not to say she will develop anything, just be cautious without becoming too anxious about it.