This question depends on the state you are in. For example: a divorce in Michigan takes 60 days without children and 180 days (6 months) with children. This time period begins from the time you first file your first papers with the court. Call your Circuit Court in your county to find out your exact "Waiting Period" or look for Divorce Guidelines for your state.
When you see your child smile and it reminds you of their other parent, say something positive. For example, tell your child "you are lucky you have dad's beautiful blue eyes", or "mom's winning smile". Telling your child that through them you can see endearing parts of their other parent will go a long way in making your child feel secure. It allows your child to know that they will always be loved, even when they remind you of their other parent. It also tells the child that you still remember the good qualities of their other parent.
Before going to ask a doctor for a prescription to alleviate your depression, attempt to work it out more naturally. The depression that comes with divorce is real; it is not a chemical imbalance or an unnatural state, so treat it naturally. Exercise, volunteer at a church or hospital, read life affirming books, or listen to uplifting music. Take control of what you can control!