You seem to be more in the style of telling a story when the scene starts, but it shifts to recounting events rather quickly. This seems like it could be the beginnings of an excellent story, but you should take this as a brief synopsis.

Watch your tense, you start off in present tense, and employ it much more effectively I must say given that this is a dream, but shift into past tense. It's imperative that you stick to one tense. And if you want to stick to the context of the entire event being a dream (Fictionalize all you want, it makes things much better then just recounting exactly how something occured!) try to include some more bizarre things to let us know its a dream and anything can go. Or if you just want to flesh the story out into something that really could happen, stick with past tense.

You don't have a problem with prose, which is very good, a lot of people like to rely solely on dialogue, but focus instead of on telling us exactly what actions your characters are taking into trying to show us what actions they are taking.

You're paragraph There is a book...sprawled on the floor is the one most guilty of sounding like the synopsis of a dream (which I gather you were initially going for) so if you decide to turn this great beginning into something make sure to stay away from that sort of thing.

Anyway, I really feel this is the seed of something that will be very enjoyable to read and if you decide to turn this into a short story or something longer, I would be eager to read it and see how things go.