Are there any cheap air quality sensors?
To detect dust, there is Sharp GP2Y1010AU0F, see http://www.watterott.com/de/Sharp-GP2Y1010AU0F-optischer-Staubsensor

It is cheap, measures particulat matter in air by reflection. But it has a huge drift, and it is hard to interpret small readings, but it worked for me up to a point. It is also not particularly sensitive - a minimum of $0.1 mg / m^3 $ is quite a lot of dust. But for the price, it is certainly worth a try. And you must read the datasheet, of course. 

Problem is, if you measure around humans, the amount of big particle dust (the kind you see blinking in the sun) is abundant, and it becomes even harder to measure fine dust. To measure fine dust, which settles way slower than the big stuff, you will have to do a measurement while you are away.

If you want to measure only the fine dust, you will have to filter that out first, and measure the particulate mass in the filtered air. That is probably not going to be cheap.