S.H.
Well... my kids, with potentially gross stuff like this.... we would research it online and SHOW them, how 'germs' and putting things in their mouth or not washing hands, can make people sick and how it is not sanitary.
So this, literal way of 'explaining' to them, worked for them.
Because it was not just 'us' lecturing them.
And they liked to learn... about things this way. By researching it.
Your daughter is old enough, to show her that way.
http://www.henrythehand.com/
http://www.earthskids.com/basic_handwashing_info.htm
Next: have you ASKED her why she sucks her hands?