Are you sure it's a 3GS? An easy indicator would be the lettering on the back case of the phone where it says "iPhone 8gb" whatever .. if it has a matte finish, it's a 3G, if it is a chrome finish just like the Apple emblem, then it is 3GS.
That aside ... There shouldn't be a problem filming video with a 3GS, does the camera/video toggle switch appear in the bottom right hand corner when the camera app is open?