On the other, I'm not sure where your 15 kg came from.
This matters, because fancy fuels matter a lot more for higher-mass or high-Δv payloads than smaller ones.
A fission fragment rocket can be Isp of 1,000,000[1] depending on the exact details — thrust is proportional to momentum (mv), not energy (0.5(mv^2)), and that means four million times the energy density is two thousand times the momentum and thrust, so that 15 kg is like 30 tons of conventional propellant: a nice saving, but you'd use a lot more than that for e.g. a manned mission to Mars.
For missions where the payload rather than the speed is critical, fuel is also a small fraction of total mass, so you also get a performance boost from being able to approximate the Tsiolkovsky rocket equation as linear.
But that's perhaps another factor of 10, which is still roughly 25% of a Starship upper stage, so even then I'd expect at least 60 kg even if the engine itself can be considered negligible in both cases.
And that's likely to be burned through much sooner than Pluto, though it depends on the details of the design. The ship would likely melt if you tried to thrust at 1 gee, but I think it would still be comparable to the Earth-Moon distance, give or take a factor of 3.
If you want something that burns from here to Pluto, then… huh, I was going to say you're likely back in Tsiolkovsky's realm, but apparently still not, and also still sub-relativistic (~ 1 milli-c for the specific values I was using).
Which is still safe, I just don't think it's quite as trivial as you say.
In fact, even though the fuel pellets are only about 1µm across, they still bump into enough atoms on their way out that the pellets heat up significantly. A major engineering consideration of the engine would be to absorb or deflect the heat radiated by the >1000°C fuel pellets without letting that heat quench your superconducting magnets.