Pedro Martínez: Is a double room one that has two beds? Or is it something else? I've re-read your sentence with and without the "a". Both ways seem OK to me, almost like it doesn't matter.

I think I am used to hearing a room with two beds just called a "double". The word "room" is what is strange to me in your sentence. A single has one bed, a double has two, and then there's the possibility of having a rollaway brought in for more sleeping space. More than one room is often called a "suite", whether or not there's any more beds in it.