What are my rights as a father in a child custody case?

I’m battling for equal custody of my 10 year old daughter and it seems that at every court hearing the judge has a preference for giving custody to her mother. I thought I had the same rights to custody as the mother but that doesn’t seem to be the case. The judge even asked me at the first temporary hearing how I thought I’d be able to handle my daughter’s needs as she gets older. I am just as good of a parent as the mother, probably better. Do I have equal rights as the father and can I get shared custody? Is there some preference that courts have in Virginia for awarding custody of children to the mother, especially if the child is a girl? What do I have to show to a judge to prove that I can parent my daughter as well as her mother can?