Not very far at all, I'm afraid. The problem is that while Jupiter supplies a huge amount of fuel, it also has a huge amount of mass, which neatly uses up the advantage of having all the fuel. Basically, it's just an expanded version of a fusion rocket and to a first approximation gets the same performance.
Take a look at the Rocket Equation: The delta V you get from a rocket is the product of the exhaust velocity (which is the same for all fusion engines) times the log of the ratio of the initial mass to the final mass. (The initial mass is the mass of the rocket plus fuel. The final mass is the mass of the rocket after the fuel has been exhausted.)
Note that this doesn't depend at all on how big the rocket is, just on the ratio of its initial to final mass. Big rockets don't fly faster than small ones or go further than small ones unless they have a higher exhaust velocity or a bigger mass ratio.
Because you're talking about a low thrust for a long time, the engines can be very low mass compared with Jupiter, and that improves the efficiency of the system. (Also, Jupiter's mass supplies its own fuel containment for the start of the voyage, so tankage may be ignored. Maybe.) Rockets are very sensitive to the non-fuel mass they have to carry along, so based on this fact, the Jupiter plus fusion candle would be somewhat more efficient than a "conventional" fusion rocket and would be able to go further.
But, when we think about parasitic mass, Jupiter is about 25% parasitic mass: By mass, it's 70-75% Hydrogen, 20-25% Helium and roughly 5% heavier stuff. The bulk composition of Jupiter is about (See the Wikipedia article on Jupiter for a bit more detail.) Jupiter's fuel is terrible for rocket efficiency! (It's like trying to fly a chemical rocket where a third of the fuel tank is accidentally filled with water.)
This second "minor" effect completely dominates the first, so Jupiter would be significantly less effective than a "conventional" fusion rocket.
So, bottom line: Don't buy a ticket on Jupiter Interstellar Spaceways.