This is how religions get started. One guy tells a lie, too many people take him seriously, and somehow it ends up filling a void in people's lives by allowing them to feel self-righteous. In 1000 years you could easily have people demanding that their Qanon conspiracies receive recognition as a belief system. They'll get offended if you call them crazy and they'll worship at altars to Q. People who point out the obvious absurdities of their ramblings will be called "Qphobes" or just "edgy teens." All the while, they'll keep waiting for Q to topple the deep state, as they have for generations-- repeating "trust the plan" over and over again, hoping for a day of judgement that will never, ever come.
If QAnon manages to stick around for a millennium then it'll have earned its keep as far as I'm concerned. Fortunately for the rest of us, though, I think it's far likelier to die with Trump, possibly even with Trump's presidency.