To have an exclusive Google Search shortcut would probably need some coding or something, perhaps a bat. file, don't know, goes beyond me.
To have direct Internet shortcuts on Desktop isn't really advisable. They may cause many troubles. I wouldn't recommend it. And besides, a Google Search shortcut won't help you, unless you have a browser running; connecting the shortcut to, say, IE would mean IE starts... we go towards reverse engineering which is a very bad thing, and illegal. Not sure about it all, but safer to stay within IE, if that's your choice for a Browser.