As a newer mbr to the board I thought I would choose the oldest muppet - Pierre the French Rat - mais oui
Pierre the French Rat was one of Jim Henson's first puppets, and the oldest surviving today. Pierre was created in a comic strip that Henson drew for his high school yearbook in 1954 -- and when he had the opportunity to create puppets for The Junior Morning Show in 1955, Pierre was embodied as a puppet made of plastic wood.
Pierre later appeared in Sam and Friends.
The Pierre puppet is held by the Jim Henson Company Archives; it's been put on display in traveling exhibits.
The original Pierre comic strip, "Pierre the French Rat Visits NHS," is reprinted in the 2001 book Jim Henson's Designs and Doodles.