Here's some VBA with error checking that will do the trick.
To use copy into a Module in the VBA editor of the workbook in question and save the file as a .xlsm file in 2010 or 2007.
Then just place your activecell cursor in any cell in the row to be moved, press Alt+F8, double-click the MoveRow macro and answer the prompt box. Note the row you enter will move down. The code should also work in 2003 but I haven't tested it so I don't know, but in any case in 2003 you just save the file you don't have to change the extension.
If you're using 2010 or 2007 the manual method would be to select the entire row, press Ctrl+X, then select the Destination row and Right-Click the row number and select Insert Cut Cells. This will accomplish what you want w/o having to go back and deleting the source row.