jaydblu,
Did you initially drag the Firefox icon onto the Applications folder in your Dock to begin with? That's where the actual Firefox application should reside. The Applications folder is a folder with a stylized "A" on it near the far right side of your Dock. Once the Firefox app is in the Applications folder, you can open that folder and double click on Firefox. That will open the Firefox browser and place a Firefox icon in your Dock to the LEFT of that little vertical divider line. Those icons on the left side of the vertical divider are kind of like aliases or shortcuts to the actual application. In order to keep the icon there, one way to do it is to simply click on it once and hold and then drag it out of the Dock (don't let go of the mouse) and then put it back in. You may see a little puff of smoke, but don't worry about it. Alternatively, you can just click and hold on the icon in the Dock and select "keep in Dock" from the popup menu.
Regards,
Steve M.