Personally, I would never write that, unless the room's ownership were obvious from the preceding context. Assuming it isn't (otherwise the question is pointless), I would leave "of her room" out of the statement altogether.
Louise and Jizanthapus were sitting on the floor. Jizanthapus leaned back against her bed, ....
With no introduction it is now strongly implied that Jizanthapus is female and that the room belongs to her. (Or at least to both the females. Later text could clear up the slight ambiguity.)
Technically, Jizanthapus could be male and the "her" could be referring to Louise. But that would jar the reader, violating a major dictum of fiction writing -- the very thing I was trying to avoid in the first place:
NEVER GIVE THE READER CAUSE TO WONDER "WHAT DOES THE AUTHOR MEAN?"
This is not to be confused with "what did that character mean" or even "what does this story mean," which are totally different. You never want to take the reader out of the story, unless your narrator is doing it purposely for dramatic effect (and you've got to be careful with that). Messing up the suspension of disbelief without good cause is a violation of the contract between reader and author.