The court will look at a variety of factors pursuant to Virginia Code 20-124.3 to determine which parent should have custody. https://leg1.state.va.us/cgi-bin/legp504.exe?000+cod+20-124.3
How long the divorce will take depends entirely on how much the two of you fight it. When both parties are in agreement a divorce can be completed within a few weeks. When parties are fighting, it can take years.
There is nothing stopping you from leaving the state, but if you take the child with you, the other parent may petition the court to the have the child returned to his custody.
As long as one of you still lives in Virginia, the divorce can be filed here. If your husband is on a ship or stationed overseas, but his last station was in Virginia, then he can be considered a resident of Virginia for jurisdictional purposes.
This answer is given in accordance with the laws of Virginia and may not be applicable in any other state. It should not be construed as legal advice, as that would require a more thorough analysis of all of the facts involved in a specific case. If you need further information or assistance, please feel free to contact my office for a consultation.
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