Would it be feasible to build a jet fighter plane based on a wooden construction?
The wings and a few parts of the body of the Heinkel He 162 jet fighter were made of plywood.
https://de.wikipedia.org/wiki/Heinkel_He_162#Konstruktion_und_Ausr.C3.BCstung

The Bachem Ba 349 'Natter', a rocket-powered interceptor, was built almost entirely of wood.  https://en.wikipedia.org/wiki/Bachem_Ba_349