There are no Greek words that start with Q. The modern Greek alphabet has 24 letters, and none of them is Q. The letters run from alpha to omega, and the sound we write as Q in English has no matching letter in the list. Because of this, you will not find a Q section in any Greek dictionary.
The reason goes back to ancient times. Early Greek did have a letter called qoppa, which looked a lot like our Q. It stood for a sound made far back in the throat. Greek speakers slowly stopped using that sound, and the letter became unnecessary. By the classical period, qoppa had dropped out of the everyday alphabet, and it survived only as a symbol for the number 90. The Romans borrowed the letter from the Greeks and passed it on to Latin, which is how Q ended up in English and many other languages.
Some Greek words come close, though. When Greek names and terms are written in the Latin alphabet, the sound “k” is often spelled with a K or a C, and sometimes people use Q for the same sound in older or unofficial spellings. Many English words that seem to start with Q, such as “quartz,” do not come from Greek at all. If you came here looking for Greek vocabulary, the best place to start is the letter K, which covers the sounds that Q once stood for.