Redwood is a pretty soft wood, but it it weather resistant. I've been looking into Alaskan Yellow Cedar (actually in the cypress family). It's highly weather resistant, but if you don't use corrosion resistant fasteners, will rust stain pretty quickly because of the resins in it.
I don't have any first hand experience with putting the bed wood in but I would think it would be possible. Probably easier though to do the job all at once.
