Can my PC cope with this screen?

I hope this isn't an abuse of everyone's helpfulness but can anyone work out if my 5-year-old Sony Vaio can cope with this new monitor I want to buy (to use as a second monitor). My laptop is a VGN-FJ3S. It has a VGA output.

Here are screen shots of what I think are the graphics card outputs (one for the built in monitor, one for the output):

Many thanks for any help you can offer.

According to this datasheet (which can be found by googling for "915GM") your graphics controller can work with a maximum resolution of 2048x1536 which is enough for controlling a 1920x1080 monitor like the one you would like to buy.