Yeah... I guess it would need to be changed from a text editor control to a grid of some sort? Then each row would represent the output of one request. I guess each row could also have the overview of the query (error/rows affected etc) on the bottom of it.
Perhaps you could leave this logging window alone and create another one that is optional to show and dock? That other one being the grid style. I'm not sure what language / framework the program is built in, but perhaps there's a 'drop in' datagrid control or an MSHTML control where you can output as a <table>.
<th><tr><td>Query Id</td><td>Query result</td><td>Duration</td><td>Affected Rows</td><td>Errors</td></tr></th>
<tr><td>#1</td><td>select * from table1</td><td>0.000 sec.</td><td>1</td><td>0</td></tr>
Of course, I'm not suggesting it is so simple, just theorising how I might approach it.