There aren`t many offensive words that begin with Q or Z. As a matter of fact,
ZAMBO+S ( offensive word for a Black person ), is the only offensive word I found,beginning with Z. There are 3 offensive words starting with Q:
QUEERCORE+S ( gay-oriented punk music ),
QUEERDOM+S (gay culture ) and
QUIM+S ( taboo word for the female genitals ). There might be more offensive words beginning with Q and Z, but that`s all I could find. Please let me know if you find some more.