from The Century Dictionary.
- noun One who kicks up the dust; a streetwalker: a term of contempt applied to a woman of low character.
from the GNU version of the Collaborative International Dictionary of English.
- noun obsolete One who kicks up the dust; a streetwalker; a low manner.
Sorry, no etymologies found.
As for "tosspots" that exclusively denote women, all I have found accuse them of immoral behavior: flingdust and flingstink, and the milder shaketail and wagtail (which is also the name of a bird that performs the gesture in a less suggestive manner).