[headquarters]

For the record , the WWII Luftwaffe had programs running that were overrun by the allies that would have meant that a continued war into 1946 could see numerous jet fighters fielded.

I refer to the excellent pages of Luft46 that has indepth material on these.

A jet engine per say is not very complicated - the V1 bombs had simple jets that actually could be made by pretty untrained personell using scavenged materials.

Building an operational combat aircraft is a totally different matter , but some type of CAS plane could be fielded with very limited resources .Although why you would insist on this being a jet instead of a prop powered one I dont understand - most hitech AAA liek SAMs and indeed much of the radar capacity would be over and done with in this stage of the war ,effectively setting the situation back to around 1945 or eaerlier in terms of anti airpower .
Also there is the question of fuel efficiency , and the advantages that props have in that regard .

If there were factions operating on a level that gave them the possibility to manufacture war supplies after TDM ,(say MilGov or the PolitBureau in what remains of USSR ), putting together a limited production of some sort of "emergency war plane " is certainly possible from a technical point of view.

The alternative being having one or two hi tech fighters with fuel for one or two operations - I would prefer having several old school fighterbombers with fuel for extended ops and aerial recce .Something like the ME-329 or other aircraft that never were -but well have been .