Your problem is not that the div is not at 100% height, but that the container around it is not.This will help in the browser I suspect you are using:
html,body { height:100%; }
You may need to adjust padding and margins as well, but this will get you 90% of the way there.If you need to make it work with all browsers you will have to mess around with it a bit.
This site has some excellent examples:
http://www.brunildo.org/test/html_body_0.html
http://www.brunildo.org/test/html_body_11b.html
http://www.brunildo.org/test/index.html
I also recommend going to http://quirksmode.org/