Brushless fans DO generate a fair amount of noise. They might not have brushes, but they do switch the coils via FETs. Since the fan probably draws less than 200mA @ 12V, I would put a 10 ohm 1W resistor in series with the fan, and a 100uF + .1uf across the fan leads. You should put the resistor and cap close to the fan (not at the end of 10" leads!). The fan will run a bit slower than normal, but I assume you can tolerate that. Cheaper and smaller than an inductor, and (for this purpose) probably just as effective.

Also be aware that your fan not only has switching coils, it has rotating magnets. Any nearby conductor (less than 3" or so). will have induced voltages.

I can't imagine getting much noise if you use the filter I described and have the fan well away from your circuit.

And I'm with Mister_e. Breadboards are no good for low noise - or high frequencies..