Default fixed-width font in Qt

Is there a cross-platform way of getting the user's preferred fixed-width and proportional fonts in Qt?

For example, in Cocoa, there is

NSFont *proportional = [NSFont userFontOfSize:12.0f];
NSFont *fixed_width = [NSFont userFixedPitchFontOfSize:12.0f];

I would like to find an equivalent in Qt that works in Mac, Linux, and Windows.