Not a Physicist here, but I do actually know a few things about jets...
So lets assume your fighter is designed aerodynamically to be able to handle supersonic speeds, that's pretty easy compared to your alternative power supply, since we have had supersonic jets for 60+ years.
As stated in the Question, that kind of propulsion system is theoretically possible but wildly impractical. For one thing, if this is a fighter and you are worried about Plasma level heat in the exhaust, no level of chaff will help you evade heat seeking missiles. What you have to do to to shield from the plasma is going to add significantly to the weight, which will slow you down. But it is not totally impossible to power a very fast jet with a small fusion engine rather than with lots of dangerously volatile fuel.
The big problem you are running into is Thrust. Can you get enough air/fuel/whatever into the aircraft and expel it out of the back end fast enough the Sir Isaac Newton gives you a kick in the pants Via his 3rd law. Currently this is done by what Aircraft Mechanics like to call Suck, Squeeze, Bang, and Blow. Jet Engine Sucks in a large Volume of air with a big fan (SUCK), uses the rotational energy of the fan to agitate the air and compresses it (SQUEEZE), Adds a generous amount of fuel and ignite it to add even more energy to the mix (BANG), and then let it all out the back end to create thrust (BLOW). Here is a bit about that: Suck, squeeze, bang, blow There are many private aircraft around the world that regularly cruise at .8 Mach and the new Bombardier Global 7500 which can get up to .92 Mach using engines that rely on that technology.
That's pretty much how a modern jet works. Now your little nuclear reactor would probably work best to supply the "Bang" Phase. It would be able to super heat the air at that phase rather than relying on a fast chemical reaction. You might be able to do that without the necessity of a plasma arc and all the attendant problems that go with playing with stuff that can reduce things to their component atoms.
In Short, use your special power supply in a way to replace a phase of the regular jet engine, and make sure you aren't making your pilots glow in the dark or dumping dangerous stuff everywhere you go. This is far more realistic than a method using heat exchanges or direct outflow of plasma