Inara wears several coats, coverups and robes throughout the series, and this particular coat (or cape) has a fur edging.
More after the break...
More screencaps from Out of Gas (worn with her Peach dress):
A similar (if not the same) coat appears in The Message (worn with her Orange and Oatmeal):
Another coat she wears is in the episode Ariel (with her Red dress):
She also wears this coat in Heart of Gold (also worn with her Orange and Oatmeal):
My Photobucket Album for Inara.
Serenifly Costumes site for Inara.