My thoughts were that they were both planning to just nap awhile rather than sleep for very long so they went downstairs. But, if Julia had to sleep upright, I think it would make more sense for her to sleep in a chair in Josette's room to be near her patient. (Of course that would have made it more difficult for Harry to slip the poison into the medication I suppose.)
What I can't understand is how Julia is still a guest at Collinwood after more than a year - or is she paying rent by this time? Either way, wouldn't someone outside of the Old House start to question why she's still hanging around?