So why isn't the sky violet?

The answer is pretty simple, but leads to an interesting area of human perception. We have three different color sensors in our eyes, all with broad wavelength response curves. When we perceive "yellow" that means our red cones and green cones are being stimulated in roughly equal amounts. We can perceive that same "color" by looking at a single pure wavelength of light halfway between the red and green cone's peak wavelengths, or we can perceive it by looking at two (or more) wavelengths of light that stimulate both red and green cones in equal amounts. (This leads to some very disturbing experiments with narrow-band filters and different light sources that look the same without the filters.)

Here's a website that has a graph of our cones' response to different wavelengths of light:
Blue is not Primary

If you look at the last of those plots, and imagine the Raleigh Scattering equation overlaid, the answer to the girl's question becomes obvious: The scattering does not produce discrete wavelengths of violet, blue, and green, but rather produces all wavelengths at attenuated intensities as the wavelength gets longer. We are sensing the violet, but we are also sensing some green. We perceive that combination as blue. It the scattering fell off more aggressively, then we would perceive the sky as violet. If it fell off much less aggressively, then we would perceive the sky as white.