Only works if Quirrell knows where to start looking to begin with. Actually, it is fun to speculate on whether this sense of doom obeys the inverse squared law or something else. Options:

1. there is a conserved "doom charge" which repels another one like it: you get inverse squared for the force of repulsion.

2. there is a "doom radiation" affecting a "doom detector": simple inverse for the discomfort level. Something like a "doom magic" source.

3. Quirrell has a doom charge and Harry is a doom dipole: this would be 1/r^3, but it does not really work since the sense of doom is not directional

4. Quirrell has a doom charge and Harry gets a "doom induction", forming a doom dipole whose strength depends on Quirrell's doom field strength: 1/r^4. This breaks the symmetry between the two, however.

5. Both H and Q get doom induction from each other: 1/r^6. This is way too steep to fit the experimental data, as it would feel more like a "doom wall".

6. There is a dissipating doom charge (because the doom charge carrier "doomon" is massive, or because of the ambient magic vacuum polarization): exponential (Yukawa) decay.

1 or 2 are probably the only likely options, with 2 less likely, both because of the need for the doom source and because simple inverse decays too slowly to fit the description.