Try to select the 1st row from the (IE selects highlights the text Firefox 3.x highlights the cells)
This is how IE works. When there is no data in table selection is invisible. It is possible however (in IE8 and especially in new IE9 and IE10) to copy empty row (it gets pasted as table). To do that just click on tag in elements path and then use Ctrl+C/Ctrl+V or use Shift+Arrow to select table cells.
Click in the new second table and CTRL+V to paste, a nested table is then inserted instead of just the row. (In Firefox 3.x you select the row and paste to get the desired effect)
I haven't observed such behaviour in FF.
An option Copy Row and Copy Column (in the right click menu) to move data between tables would be the ideal solution.
Taking this last comment into account, I'm changing this to feature request.