Resolution with an external monitor

I just started using my MacBook with an external monitor, and love this new set up. But, I have a quick question. When I hook it up, my screen looks like an enlarged version of what's shown on my smaller MacBook screen. This is okay, but I'd like everything (dock, menu bar, etc) to be the same size as on the MacBook screen, only with extra desktop space, if that makes sense. Currently, since everything is just enlarged, I don't feel like I have any extra screen real estate - windows and the dock take up the same amount of space relative to the screen size as they do on the MacBook. My resolutions are 1280 x 800 on the MacBook and 1280 x 720 on the external monitor. I tried playing around with different resolutions but keep getting a No Signal error on the monitor when I use anything else. I know this is kind of a difficult question but does anybody have any ideas?

 

Using a 19" Element flatscreen I randomly had lying around the house (not the best, or even a real monitor, I know ), connected to my mini-DVI port - using a mini-DVI to DVI, which is then connected to a DVI to HDMI, which is plugged into the back of the screen. And yes I am mirroring. Considering this isn't meant to be a monitor, I'm guessing it'll probably have to stay this way??