Thanks a lot!
Now I think I got it.
I basically, in the end, after canceling out the same stuff on both sides of the reaction, was left with:
2 ClO3- + 2H+ --> 2ClO2 + 1/2 O2 +H2O
I returned to the molecular formulas and also understood that those two hydrogen atoms on the left were coming from the sulphuric acid. So I just converted 2H+ into H2SO4 and, clearly, added again K2SO4 on the right.
2 KClO3 + H2SO4 --> K2SO4 + 1/2 O2 + 2 ClO2 + H2O
Alternatively, if one doesn't like the half integers, they could just multiply everything times two.
Is this correct?