You do not FILE for separation in Virginia. You can sign a separation agreement, but a written agreement is not a requirement in order to be separated or ultimately, divorced. You can work out the terms of this agreement using mediation. The mediated agreement then would be made a part of your Final Decree of Divorce. You still must file a Complaint for divorce in court and follow your local jurisdiction's procedure to finalize the divorce, which may include a court appearance. You must satisfy all statutory requirements in order to be granted a divorce. Failure to do so would be the only reason that a judge would refuse to grant a divorce.
Courts encourage mediation and the use of mediated agreements.
Mary Commander did a great job answering your question. Among the issues that arise when you prepare to file is whether you have lived separate and apart for the statutorily prescribed time, whether you actually both signed a separation or stipulation agreement, whether you have lived in Virginia for six months immediately preceding the filing of the divorce, whether the court has personal juristiction over both of you if you are seeking anything (support, custody etc). Probably worth your while to have an initial consultation with an attorney to make sure all the bases are covered.