QTStreamSplicer is a tool that allows you to splice a still picture onto the front (before the live stream starts) of a live streaming movie. Select "Splice Image Onto Stream..." from the Splice menu, then select (first) an image file and (second) a streaming movie file; then select the desired options in the dialog box that is displayed and click "Splice!". You are then prompted for a location to save the spliced file into.
QTStreamSplicer also allows you to splice a still picture over an audio-only streaming movie. Select "Splice Image Over Stream..." from the Splice menu, then select (first) an image file and (second) an audio-only streaming movie file; then select the desired options in the dialog box that is displayed and click "Splice!". You are then prompted for a location to save the spliced file into.