Well, you cannot launch it from the dashboard since that is an application itself (tied to F12, press it sometime, that is the dashboard) I think you mean the dock.
You will want to change the default download location for your browser (hit Apple + , to bring up preferences) and then when you download a .dmg, just drag the application icon to the applications folder and you will be set. It really does not matter where most apps are installed, and you can move them whenever you feel like because of the fact that the application is actually contained inside the icon, if you were to view it under windows or linux, you would see that it is actually a folder, it is just a special folder that launches its contents when double clicked, pretty cool if you ask me.
Just go ahead and move the existing apps from the desktop to the applications folder (make sure first that their associated dmgs are unmounted, I have found in the past that although the icon is on the desktop, the application is actually running from the dmg, so when you unmount it, the app is no longer usable) and you will be fine