Plex matches against TheTVDB.com, which shows these as separate episodes.
Doctor Who - - Season 1 - TheTVDB.com
Following their naming, your file names would be:
Doctor Who - S01E01 - An Unearthly Child.ext
Doctor Who - S01E02 - The Cave of Skulls.ext
etc.
This should work. Point the TV library at Doctor Who, not at root. Pointing at root will confuse Plex (and no other library can point at root either). Alternately, you could individually add the 1963 and 2005 folders to the library.
If you move/rename files, whether movies or TV shows, you need to perform the Plex Dance to ensure Plex has the correct file location, metadata, etc.
