Child custody

I and my wife have been married for two and half year and have nine month old baby girl. Around a week back we had a fight and she left home with the baby alleging that my family used to harass her and I used to beat her regularly, which is not true. I am thinking of talking of her and resolving our differences. We both our engineering graduates with MBA in marketing and earn more or less same. My immediate family consists of my mother and father. Her family consists of only her mother, who is handicap with a slight limp. Her mother and father do not stay together and the her father stays with his first wife. I have the following question 1. Supposing my wife refuses to come back can I fight for the custody of the child as my wife's mother will not be physically capable of looking after the child as my wife is a working professional. And in case my wife decides to resign from her job to look after the baby she will not be financially capable to look after the babies needs. 2. As per her allegation of I beating her regularly and my family harrasing her, it is my word against her's. We did have our share of our fights but nothing major. Will it have any impact in case I decide to fight for the child's custody. 3. As per my knowledge for a child below five years, the custody will be automatically given to the mother regardless of the circumstances. Is it true? And will I be able to fight for custody of my baby only after she turns five year old?