You are a member of a tightknit crew struggling to live life your way on the fringes of space. Each day is a struggle to maintain your life, your ideals, and the lives of your friends. Dogs seems to be the perfect vehicle for this type of Wild West Space drama. Here are the conversions (off the top of my head:)
One (or more) of the PCs owns a ship. He is the captain. How he captains is up to him, but ultimately it is *his* ship with all of the good and bad that comes with. All of the Players should agree as to who is the captain during character creation.
Character Creation is pretty standard. Choose a type, assign dice, pick possesions, etc ... Each player must have a tie to either the ship or to the captain (just as each player in Dogs must have a tie to the Dogs.) For example, "I am a member of the Serenity's crew."
As GM you create Jobs instead of Towns. The Players arrive somewhere for a Job. Here are the details and some NPCs. What aren't they being told? What is really going on? What are the complications?
Adapting the Faith: This is where is gets tricky for me. The players are not enforcers as per Dogs (or any of his examples) but I see no reason why there couldn't be several sets of Faith that PCs could or could not choose to call upon. For example, there could be the Faith of the Shepard, the Code of the Brownshirts, or Pyschic Mojo. That being said, who said the PCs are on the fringes and not enforcers of some type.
It looks like there is going to be a Serenity RPG coming out, which would be useful for Source Material (the system looks fine, but definately more cinematic than gritty.)