Q is derived from K (it's a thin wrapper that uses words instead of sigils for some verbs), which is derived from APL; J is a completely separate lineage, also based on APL.
http://www.jsoftware.com/jwiki/Essays/Incunabulum
http://keiapl.org/rhui/remember.htm
http://www.jsoftware.com/jwiki/Essays/Incunabulum
http://keiapl.org/rhui/remember.htm