Cat you are mostly right. There is no actual document Q. It is the hypothetical document that parts of Matthew and Luke are based off of which Differ from Mark. Matt and Luke are very similar to Mark but some parts are unique to each and some parts are unique to each other but not in Mark.

This is the prevailing theory that I have heard:
Mark
L- Luke :Q: Matthew- M

John

Best diagram I can make here. Basically Mark and John are unique. Luke and Matthew both have material from Mark and from a hypothetical document Q. Luke has material unique to itself from hypothetical document 'L' and same with Matthew from a hypothetical document 'M'.
I think some people have published a book which they call Q but that is only a compilation of the things found in both Matthew and Luke. It would not surprise me if such a published book did not explictly say that but hid it in a lengthy introduction that few would read.

Godspell trying to be useful