Don't know how you expect a table to automatically copy? You'd have to hand select the table copy it and go back to the document and place it.
You can use CTRL TAB (I think it's CMD ~ on Mac) to switch between open docs. Holding shift while doing this goes the opposite way.
Or you could select all the text in the document with the Tables and paste it into the Pasteboard on of your working document. Deleting text/tables etc. as you go along.
I was thinking something along the lines of a macro/script? Not really sure, I don't know ID that well. If there is no better way that is OK. I just don't want to kick myself for not using a more efficient method.
If you don't want to take up screen real estate then I say switching inbetween docs using keyboard shortcuts would be efficient.
Or as I say copy all the text from the other document and place it on the pasteboard and you grab the content as you move along the document.
Other than that - I don't know how a script could target the specific table in another document?
Perhaps it could be scripted? Have you tried the Scripting forum?
Well, all of the prebuilt tables can reside on the pasteboard of the same document, if that helps.
But I think you are right. I can just switch between documents. It's not that bad.