Can't find out much history about the music and lyrics, but the work as a whole is credited to Dave Kahn, Melvyn Leonard, and Mort Greene.

Hey! Here they come with a rum-tee tum they're having a toy parade.
A tin giraffe with a fife and drum is leading the kewpie parade.
A gingham cat in a soldier's hat is waving a Chinese fan,
A plastic clown in a wedding gown is dancing with Raggedy Ann.

Fee fie fiddle dee dee they're crossing the living room floor
Fee fie fiddle dee dee they're up to the dining room door.

They call a halt for a choc'late malt or cookies and lemonade
Then off they go with a ho ho ho right back to their toy brigade.


source: http://www.lyricsondemand.com/tvthemes/leaveittobeaverlyrics.html