Tom Baker as Dr Who
The Doctor informs the Council at Galiphree that he is leaving for his scheduled vacation, to get some R&R. Brandishing a walking stick, he announces that he looks forward to getting some exercise and fresh air. They bid him farewell, and he departs in his TARDIS.
The TARDIS then soon materializes in some small innocent-looking rural village. The Doctor steps out, and is warmly greeted by a group of small furry-footed fellows, with cries of "Gandalf! So nice to see you back!" The Doctor (Tom Baker) looks into the camera and grins mischievously...
<cue to the intro theme music...>
Brainstorming for story ideas:
The Master, the Doctor's archenemy, would take over Isengarde, the domain of Saruman. Heh, I'd love to see The Master (played by Anthony Aimsley) going "my precioussssss," wanting to keep the Ring all for himself. I can also imagine a scene where the forces of good march victoriously on Isengarde, only to see the tower Orthanc disappear while making the TARDIS noise.
Sauron himself could be either a Dark Guardian, or some other enigmatic evil.
While Frodo would be The Doctor's main companion in the story, K-9 would of course be along for the ride. K-9 could heat up the Ring with his laser beams and decipher the inscription on it. He would also be convenient for zapping Orcs along the way. Another repeated sight gag would be the Doctor pretending his plain old walking stick was magical, and then quietly using his little instrument doohickey, that he takes out of his pocket, to do any real "magic".
I was thinking about the Daleks moving thru a gorge screeching "exterminate!", only to be swept away when the elves summon a flashflood.