No, the musical composition itself (i.e., what you might express tangibly in sheet music) has copyright distinct from the copyright that exists on Led Zepplin's recording of the song. Your new cover will still be a derivative work of the musical composition.
When you record a cover of a copyrighted song, you must get permission from the composer (or current copyright holder of the composition). In the United States, however, you can compel the copyright holder to grant you license under 17 USC §115. Under a compulsory license, you pay a fixed fee per copy of the cover that you distribute (currently 9.1 cents), and the copyright holder must allow you to distribute those copies. See the circular Compulsory License for Making and Distributing Phonorecords from the U.S. Copyright Office. I am not aware of other countries that have a similar compulsory license scheme, so in those jurisdictions, you would need to negotiate a license with the publisher or an intermediary agency they use.
However, even if you did get a compulsory license to distribute your cover song, you must get permission to synchronize the song with a video. The American Society of Composers, Authors and Publishers describes the copyright holder's exclusive synchronization right:
A synchronization or "synch" right involves the use of a recording of musical work in audio-visual form: for example as part of a motion picture, television program, commercial announcement, music video or other videotape. Often, the music is "synchronized" or recorded in timed relation with the visual images.
Since the synchronization right cannot be acquired under a compulsory license, you will need to have the publisher (or whoever the copyright holder is) agree to license the synchronization right to you under whatever terms the two of you can agree upon.