Copying and pasting from one location to another does not always work out. The screenshot above is a copy and paste from a table in Moodle into a Google Doc.
Under table properties you are able to change the border color, border width, cell background color, vertical alignment and column width and height.
One thing I am waiting for with Google Docs is a 2 column layout. This is particularly handy when making worksheets. One trick is to create a 2 column, 1 row table. Right click on the table and change the table border to clear.
Hint, before you insert the table hit enter a couple of times so that you retain your document formatting. I try to always hit enter several times before I insert anything (pictures, copy paste, etc…) because sometimes the formatting can get funky and it is challenging to get it back otherwise.