TRADITION VS SCHOLARSHIP
The answer
Disagree. Q is the name for a lost collection of sayings that Matthew and Luke may both have used. Luke has usually been dated close to Matthew, partly because on the Q view Luke shows no sign of knowing Matthew. If there was no Q, Luke could be dated well after Matthew, perhaps even into the second century AD.
Why it’s interesting
Luke speaks of Jerusalem "surrounded by armies" (Luke 21:20), and so is usually dated after the Romans sacked the city in 70 AD. How long after is the part the Q question touches.
Genuinely debated
Learn the Bible.
Not just the stories, but the history, authorship, and scholarship behind it.