I don't know a cloud based software for this, but have used SweetHome3D (Java, so all platforms) and found it good.
You can't upload that image into it as far as I know, but building the walls is an easy task (I did it in under 30 minutes, including the learning curve).
You can then place the furniture from their stock images onto your floor plan and get a 3D perspective on it. That way you can not only measure if it would fit, but actually get an impression on how it would look.
I don't have the program anymore since my flat is now in a completed state so I can't share my own screenshots. I will give some from their gallery.
The program is available in a huge set of languages, I've used the German version.
The only downside I found was that the rooms seemed more crammed in the program than in reality, but I don't know if that is due to different perspectives.