Washing leather at home, sure. Washing down at home, sure. Washing the two together? I would not.
Any conditioner you put on the leather is going to be no good for the loft of the down (assuming this is down and not synthetic -- but synthetic fill can be even less resilient and lose loft more quickly than down). I would spot clean carefully and take it in to get cleaned professionally about once in a million years.
Otherwise, it is super fab!