Others have got this worked out, but to clarify how to do it...
enter the date you want to use in a cell and press enter, goto format cell for that cell and change the format from date to general and the date you've just entered will turn to a number (from your example, 15/12/2011 will turn into 40892), make a note of this number and then you can change the format of the cell back to date.
then goto the cell you want to perform the conditional formatting on and use the formula =$A$1=40892 (assuming the date is in A1) and set the formatting to be what you want, click OK a few times and it should work.